You are certainly not alone in having a little trouble! These terms are used by Nietzsche in his Birth of Tragedy, which was his first published book. It is important to keep a few things in mind when reading this book. First, Nietzsche’s explicit intent was not to talk about the Greeks at all, but rather to talk about the contemporary European scene by way of a complex historical analogy with Greece. Thus, it is not even clear whether any particular artists that Nietzsche may have had in mind are to found in ancient Greece, or 19th Century Germany. Second, Nietzsche is employing a fairly conventional anthropological notion: that deities and myths are ideal representations of underlying cultural trends. Thus the Apollonian and Dionysian as concepts stand for trends or forces in Greek culture rather than specific cultural products. Third, Nietzsche is also not particularly interested in the Apollonian or Dionysian in themselves. He becomes interested only insofar as these two cultural forms work together in the specific phenomenon that is Greek tragic drama. Fourth, he is not even interested in tragedy as a genre, performances, or set of extant texts, but rather in that it deals with a set of metaphysical propositions (most of which are borrowed from Schopenhauer) and reveals in Greek culture (and perhaps in modern European culture) a capacity to understand and deal with the truth of this metaphysics. Nietzsche sees the Dionysian primarily in music and the Apollonian primarily in the plastic arts such as architecture or sculpture but, for the reasons we just suggested, he names few names. Shortly after writing this book, Nietzsche distances himself from both Schopenhauer and the artist he celebrated in the Birth of Tragedy (Richard Wagner). The concept of the Apollonian largely drops out of his philosophy leaving a substantially different notion of the Dionysian.
No, I doubt we should generally regard philosophy as art, though 'art' is such a wonderfully broad and diverse category that doubtless there can be overlaps. Certainly bits of philosophical text, and/or philosophical ideas can be part of an artwork (I remember seeing long passages of Wittgenstein reproduced as part of an artwork). I hear your question as invoking fascinating issues about the status of the discipline of philosophy. Firstly, (like art) it's not an empirical enterprise, and yet (unlike most art) it is answerable to matters empirical: if a patch of philosophy of mind turns out to be at odds with new discoveries in psychology or neuroscience about how the brain relates to psychological states, then the philosophy has to adjust); and philosophy's power to explain the phenomena it takes as its subject matter (linguistic, mental, ethical, political, metaphysical...) is surely dependent on its being empirically plausible at all those points where it purports to describe our practices and their point. Second, (unlike art) most philosophy is strictly bound by the discipline of rationality: philosophical positions are meant to be advanced as arguments, so that if their premises are false, that's a reason not to accept the conclusion, or if there is a false inference, that too is a reason not to accept.
On the other hand, it is philistine (in my view) to dichotomize philosophy and more artistic - notably, literary - aspects of culture. Some philosophy has conducted itself as if it purports to be like science, which is absurd. Philosophy is, or can be, a more creative enterprise and this can only be disguised by any attempt to model it on science. But I do not believe it is a creative enterprise in the manner of most art work. Philosophy's creativity is founded on the attempt to make explicit and make sense of naturally arising intellectual puzzles - puzzles that arise out of contradictions or tensions within our everyday concepts and practices (e.g. how come we take ourselves to know things, even while we also seem to take knowledge to require absolute certainty, and it also seems to us that we almost never possess absolute certainty?); or our everyday ethical interactions or attitudes (e.g. why do we accord humans special ethical status over animals? should we? why? or how far?). This kind of making-sense activity is the font of philosophy (in my view) and (a) art is not always aiming to make sense of things at all, and (b) even when it is aimed at making sense of things (as fiction very often is, for instance) I believe that the way it does that is fundamentally different because of the absense of what I described above as the discpline of rationality. Argumentation is a distinctive activity, a distinctive method of making sense of things, and that method is generally (happily) foreign to art.
Aesthetic appreciation means well-informed, skilled and close attention to a work of art, all of which can be improved by various types of education. It may be that philosophers of aesthetics tend to not use the word 'appreciation', but the constituent ideas are certainly important. Have a look at previous answers on this site under the heading of 'art': quite a few of them concern context, culture or knowledge.
As your examples suggest, different works of art and even different artistic media can require different kinds and amounts of knowledge about the world, and about the specific context in which the work of art was created. Some works are highly accessible -- a wide variety of audiences can engage with them without any specialized background knowledge; while others require pretty deep immersion in a specific artistic tradition and practice. This suggests that not all art is equally "all about context". (It also relates to, though it's distinct from, the distinction between "popular" and "high" art.)
The next important question is what sort of context is appropriate for properly appreciating and evaluating art. In the 20th century, this question was debated most vigorously in the context of literary interpretation. 'New Critics' argued that knowledge about an artist's specific intentions in creating the work, and the specific context in which he or she created it, are (or should be) irrelevant to appreciating and evaluating it; the classic argument for this view is Wimsatt and Beardsley's article "The Intentional Fallacy." "Reader-response" theorists argued that each reader or viewer creates or "performs" his or her own work of art, because each person inevitably brings a different background to their encounter with a work. Because each viewer can only evaluate the work of art they encounter, many different evaluations of what we might intuitively call "the same work of art" can be appropriate. (One classic statement of this view is in Stanley Fish's essay "Is There a Text in this Class?".)
My own view, which is fairly common, is that we shouldn't just rest with our own immediate response to a work; one reason we value art is that it can take us out of our own immediate context and acquaint us with other perspectives and experience. Instead, we should try to respond to the work in the way that the artist intended. In order to achieve this response, knowledge about the specific context in which the artist created the work, and his or her intentions for doing so, is often relevant. But the standard for evaluating a work's success isn't just whether an artist was successful in achieving his or her artistic intention; it also matters whether that was a good intention to have in the first place: whether the work is interesting, provocative, beautiful, rich, or otherwise aesthetically valuable. It's also possible for an artist to be self-deceived or otherwise wrong about what the best response to his or her work would be; in this case, we may care more about the response that an "ideal artist" would have intended us to have. (For more on the role of the artist's intentions in determining the appropriate response to a work of art, specifically literary art, see http://www.blackwell-compass.com/subject/philosophy/article_view?article....)
I think there are actually two questions here. First, the question about the value of 'subtlety'; second, about the value of 'showing' rather than telling. In other words, I'm not convinced that the latter is a definition of 'subtlety'; it seems to me that one can tell with subtlety, and show crudely. So, with apologies, I’ll just look at the showing/telling distinction.
We’ll define ‘telling’ as straight-forward, careful, factual (or apparently factual) description. Showing, by contrast, means somehow to make the subject-matter seem real to us, as well as to make it seem important, affecting, and interesting. Since the subject may not be real at all, this involves creating an illusion. Probably the two are not entirely distinct: it may be impossible to show without also telling something.
Now, what you call 'telling' is valued in many areas: in journalism, science, history, documentary film-making, and so forth. I suggest that an answer to your question may also be the answer to the question of why these types of activity are not normally considered 'art'. The most famous answer comes from Aristotle. In his Poetics Aristotle argues that poetry (which we’ll have to take to stand for all art and literature) is ‘more philosophical’ than history, because the former deals with ‘universals’ while the latter deals with factual particulars. Roughly, he means that poetry has meaning or significance beyond its narrow setting; history is just a record of what happened. So, a play about Oedipus might have something to tell us about the nature of man, of knowledge, of faith, or of destiny. It might also have an emotional impact that a telling of the story would not. (This is probably an impoverished view of the discipline of history, by the way.)
One, but only one, of the reasons that poetry (and art) can do this is because it tends to show rather than tell. The meaning and significance of poetry is clearly related to the effects of showing discussed above.
A good question. Every human production seems to have criteria according to which it can be judged successful or unsuccessful. For example, the 'latest Ben Stiller' movie is intended by its makers to make people laugh (at the right times), feel good, and thus buy cinema tickets and DVDs. The consumers are by and large happy to agree with this set of criteria. A product that matches its criteria is 'successful'. A film that everyone agrees is a comedy, but at which no one laughs, is unsuccessful.
One problem arises when there is disagreement about success: one critic finds a movie funny, another finds it boring. Another problem is when more than one set of criteria are in use: the director wants to make a film about an issue, but the studio wants to sell tickets. Ben Stiller wants to play a serious role, but his public just want him to be funny. A comedy is deemed funny by many, but is condemned by others as demeaning to some group (thus, it is ‘unsuccessful’ according to criteria that include issues of respect, compassion or understanding).
So, a dumb movie that was intended to be dumb is successful. ‘Success’ is an ‘adjustable’ measure, as you say, and everyone accepts that. But being successful and being ‘art’ are two different things. Whatever is meant by ‘art’, it will not mean success according to adjustable measures of success.
Yes! Even if we agreed that a 'real emotion' was a necessary feature of all art (and that's a big 'if'), it might not be the only feature. For example, the emotion would still need to be well expressed or communicated; the product might need to avoid being banal or commonplace; we might think it needs also to show or teach us something.
I would like to add that, supposing art does have something to do with emotion, there is still much to recommend Wordsworth's notion that poetry at least should have its origin in 'emotion recollected in tranquility'.
I agree that an alien race that differed considerably from us would be unlikely to rate our art and music the same.
However, this does not, by itself, show that there is no objectivity in artistic value. If one wished to defend the objectivity of artistic value in the face of such evidence, one might use one of two strategies. (I) One might argue that the alien race is simply mistaken in its value judgements; for some reason---which one would have to independently specify---the aliens get it wrong while we get it right (or vice versa). Alternatively, (II) one might argue for the conditional claim that if the alien race truly understood our art and music, then they would appreciate it; evidence that they do not appreciate should be interpreted as evidence that they do not understand it. Again, one would have to independently specify some reason why the aliens do not understand our art and music.
Without more detail on the aliens and their disagreement with us, it is difficult to say which, if either, strategy would be possible.
A great question! There may be a middle ground to the answer. Beautiful natural objects, and beautiful poetic objects, might both be considered beautiful because of complex or harmonious formal properties that evoke certain responses (this is, roughly, Kant). If this is the case, the a beautiful poem about something ugly would function differently from a beautiful poem about something beautiful. In the former case, the beauty would be purely formal; in the latter, it would be in part representational.
Again, a great question, although I suspect it might also be misleading. Many well-known poems about nature are not actually about nature in a straightforward sense. Poems are rarely like landscape paintings. (Come to think of it, neither are landscape paintings.)
Great works--and also not-so-great works--are a bit like children to us. We bring them into being as a result of our desire, we do our best to nurture and to preserve them, and to advantage them in the world as best we can...and then we turn them loose into a world that may love or hate, may celebrate or destroy them. Once our children (fleshly and otherwise) are "out there," we have little to no continuing control over how things will go for them. And the surest thing of all, I'm afraid, is that not everything will go well for them.
I will venture to advise you that so long as you are fixed on how your work will be received by others, you need not worry about producing anything Great. Indeed, the greater the work, the less likely it is, I think, that the work will be received or understood both completely and very generally. If there is true greatness within you--or if some great Muse (take that any way you will!) elects to speak through you--then the Great Work will be created only because of the greatness that motivates it. It will be celebrated, scorned, or treated with indifference--each reaction showing something only about the one so reacting, and signifying nothing at all about the work itself. Do not concern yourself with such things, for you have absolutely no control over them. If you will produce some Great Work, then first find the greatness--and then fasten your seat belt as it shows you where it must go.