I'm not quite ready to accept your terminology, but will try to respond in spite of that. I think the most obvious difference between ordinary perception and things like hallucinations and dreams is that the former sorts of experiences are reasonably assumed to be verific (that is, to tell us something true about the world), whereas the others are not verific, or at least are only very unreliably so. The fact that I dream that such and such is the case (assuming I have no reason to think that I am some kind of dream clairvoyant) is of course compatible with it really being the case...but gives me no grounds for believing that it really is the case. The fact that I perceive something to be the case does give me grounds for believing that it is the case. I am not claiming, of course, that perception is infallible, for it plainly is not. What I am claiming is that there is evidenciary value in perception that is lacking in hallucination, fantasy, dreaming, and other such experiences.
I see the laptop on my desk. This seeing entirely depends on some fabulously complicated neural shenanigans in my head. The three-dimensional laptop certainly isn't in my head. But what about my perception of the laptop -- is that in my head? I make a fist. Its existence entirely depends on the operation ofparts of my body. Is the fist inside my body or part of it, as my liver is?
Nothing gets "constructed in your brain". This is a loose (if natural) way of speaking that can get you into trouble. If we open your brain, we will find nothing there beyond neural matter -- no images, no portions of visual space. The activity of your brain does make possible your apprehension of the world around you, but it's certainly not to be identified with what's apprehended. The three-dimensional world that I perceive does not exist in my brain, optic nerves, retinas, etc., even though it's true that I could not perceive it without the latter. In fact, I would go on to say that my perception of the world also doesn't exist in my brain, optic nerves, retinas, etc., though I also agree that those perceptions would not exist without all that neural activity. (For a related discussion, see Question 890.)
In perception, you are affected by the rock. You are changed, and the rock is the cause of the changes. Change means that you acquire some different properties. Now, some of your properties are intrinsic and some extrinsic. Philosophers have a hell of a time trying to explain that distinction clearly, but, roughly, an intrinsic property of something has to do purely with the situation "inside" it as opposed to elsewhere. Since your conscious states, and other sensory and cognitive states, are changed, you have undergone intrinsic change, and, as you say, your new intrinsic states bear information about the rock in virtue of its having caused them.
Now, the rock is also changed intrinsically by the encounter. Your gravitational attraction affects it some, and light bouncing off you hits the rock and changes it in various slight ways.
Unlike you, however, the rock is unable to collect and decipher the traces of your presence that impact it, and so your effects upon the rock's intrinsic properties are subtle and diffuse. However, the encounter has also changed some extrinsic properties of the rock: it now has the properties of being perceived, of being thought interesting, and so on. The rock has no clue of this, but in fact you have elevated it into participation in the world of thought.
‘Sense data’ refers to the images. The idea is that objects in the world impinge on our senses and this causes us to perceive images. We are have immediate and full knowledge of these images (although not of the objects that cause them). Philosophers who believe in sense data disagree about whether or not we can gain knowledge of objects in the world starting from sense data. Some philosophers think that the whole idea of sense data is wrong-headed, arguing, for example, that we aren’t in fact fully aware of our ideas, that what we’re aware of in perception is objects in the world, that there is no way to have knowledge of the world if we have to gain it through the ‘veil’ of sense-data. This is just a quick answer. You might also look at the article on the topic in the online Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/sense-data/
A relational property is a property a thing has only in virtue of how it is related to something else. A common example is fatherhood. Whether I'm a father depends upon my relation to something else, namely, my child (if I have one). So the claim is that, in so far as the car appears to be small, its apparent size is merely a relational property. It is, for example, a matter of how large a portion of your visual field the car occupies.
Moore's point was that it's not the car itself whose size changes as it recedes, but only how large a portion of your visual field the car occupies. Now, it's certainly true that one is given to describing this phenomenon by saying that the car gets smaller. But, of course, one doesn't really think the car itself gets smaller, and there is an obvious sense in which it seems to remain the same size but to get farther away. To suppose there is some contradiction here is to suppose that how large an object appears to be is a direct function of how much of the visual field it seems to occupy, and that's simply not true. (There are well-known visual illusions that demonstrate the principles at work here.)
Sometimes, philosophers use the term "theoretical" to apply to certain statements in a scientific theory. Sometimes, they use the term to apply to certain entities whose existence is postulated by a theory, viz., those entities that are not directly observable. In the latter sense, they are contrasted not so much to "non-empirical" entities, but to observable ones. There is a lot of dispute about what "not directly observable" means. Are entities that we can see only with a telescope "directly observable"? Only with a microscope? Only with my glasses on? This kind of continuum has led some philosophers to declare that all entities are in principle observable. And others to hold that no entities are directly observable except "sense data", categorically unmediated sensory experiences. If you do think there are theoretical entities, or that most mature sciences contain statements with terms purporting to refer to them, then a major issue in the philosophy of science is what to make of (how to understand) such statements. Are they fully meaningful? How are we to understand their meaning? Are they true or false? Can we have evidence for their truth?
Perception is not ingestion: when you see a tree, the tree does not enter your brain. Moreover, seeing does involve the creation of an image on the backs of your eyes. But it does not follow that you only ever see an image. Maybe an analogy to a photograph will help. A photograph of a tree is an image; but it is not a photograph of an image, it is a photograph of a tree. Similarly, seeing a tree may involve an image of the tree, but what we see is the tree, not the image.
The popular dispositional theory of colour that Richard mentions has a curious consequence. If being red is just being such as to tend to produce a certain kind of sensation in us, then it isn't even possible that what tends to look red to us isn't really red but is really say some shade of gray. For on the dispositional view, red just is tending to look red.
I certainly do not think that our only view of reality can be via experience by our own physical senses. Human beings are magnificently complicated cognitive beings, capable of using not just our immediate senses, but also memory, interpersonal communication, abstract reasoning, and other processes by which to form beliefs. Of course, some of these are more reliable than others: wishful thinking is highly unreliable; vision is much more reliable. But the use of expert testimony--especially when corroborated by other kinds of evidence (as for example, regarding the Taj Mahal, where you can also find photographs of it, accounts of it in narratives, etc.) can also be highly reliable--otherwise, most of us wouldn't read newspapers, right?
So, I think my answer to your (1) should be clear--I think you can have very reasonable beliefs about the existence of the Taj Mahal even though you have never actually visited it. Indeed, some of those very reasonable beliefs might lead you to decide to visit the place someday. Such a decision could hardly be reasonable, indeed, if not having already been there left you with no good reason to suppose it actually existed!
As for your (2), as my own sight and hearing have started to fade from my younger days...I'm afraid I have to agree that, on some issues and lacking any other evidence, those with sharper senses are going to have more accurate views of reality than I can have. That's one of many reasons why the other sorts of evidence are useful!
As for your final comment, as I said, wishful thinking has proven to be a highly unreliable way to generate true beliefs. On the other hand, if it works for you in the way you suggest, my college always accepts donations!
There are tensions here, I agree, though I think they reside in the way that we talk about appearances rather than in the appearance/reality distinction itself--at least as it applies to cars.
Size is an intrinsic property of a car if any property is--that is, a car's size, like its shape, depends entirely upon the way it alone is, and not upon what may or may not hold in the world around it. Apparent-size, by contrast, is a non-intrinsic or relational property of a car, and subtly so: a car's apparent-size depends not just upon the car's size, but also upon the relative location of the relevant viewer. Thus, the car's apparent-size (to Fred) can shrink if the car shrinks in size, but also (and using less magic) if Fred and the car move apart so that light from the car subtends a smaller angle in Fred's visual field (as they say). So, one and the same real car can consistently maintain its size and change its apparent-size through changes only in the relative position of the viewer.
This is all pretty obvious once it's pointed out, but interestingly, it remains a source of confusion nevertheless. This is probably because our judgment of a car's apparent-size seems to come straight from our perception of the car alone, and so to present itself from the inside as if it were an intrinsic property of the car we see. And it's this, I think, that gives rise to your second worry: the only type of size real cars have is the type that doesn't generally change when they drive away; but there's another type of size--apparent-size--that does change; and so, there must be something other than a real car--perhaps a "mental car" or an image of the car--that undergoes a change in this type of size.
But here's where we need to remind ourselves that the real car can undergo a change in apparent-size, while maintaining its size and all its other intrinsic properties, simply because a change has taken place in its relation to the viewer. This is no different than the way I can become an uncle without undergoing any intrinsic change--in fact I can do it obliviously and in my sleep while my sister does all the work in a maternity ward across the country. Unlike uncle-hood, however, apparent-size may not appear from the inside to be changable in this extrinsic way. But it is.
(By the way, how exactly we should draw the distinction between intrinsic and extrinsic properties (and whether the distinction is fully determinate) is a deep philosophical problem. But the point I'm making here doesn't really rely on this distinction so much as on the claim that apparent-size involves one more degree of relationality (or one more relata--a viewer) than does size simpliciter. The point generalizes to relational properties like closeness: the apparent closeness of Jack and Jill to one another depends upon how close together they are and upon their relative distance from the relevant viewer.)
Your first question brings out an additional complexity in our talk of appearances. You ask: at what distance does apparent-size equal real size? If you're asking for a comparative measurement, I'm inclined to reply that one can't be made. Size and apparent-size are different properties (with different degrees of relationality), and so the question makes no more sense than asking when a thing's mass equals its weight. But there's another interpretation, involving a related sense of "apparent", on which your question makes good sense. Sometimes we use "apparent" and "apparently" to mark the properties an object seems to have in perception when we recognize or even know that its actual properties may differ. The stick in the glass of water is apparently crooked even though we know that it's straight (because we're familiar with this illusion). In this sense, the apparent-size of the car is the same as its actual size when the size we perceive it to have is the same as its actual size. Compare: the apparent crookedness of the stick is the same as it's actual crookedness, because there is, it turns out, no water in the glass.
The puzzle that arises out of all of this, though, is how we should distinguish a feature that we perceive something to have from a feature we judge it to have all things considered--including not only what is given to us by perception, but also the various other things we know about the situation at hand, and about the way the world works generally. The distinction seems unproblematic in the (original) case of the stick in the glass of water. We have no problem saying that we perceive the stick to be crooked, but that we do not judge it to be so. And that in this case our knowledge of the illusion overrides the verdict of our perception in our judgment-formation. But what do we say about cases where we accommodate to the odd way that seen properties might display themselves in our perceptions, and then see right through this? Suppose I watch cars drive along a distant road. At first, they're mere dots on the horizon, but I soon get used to judging their relative sizes, and do so accurately. Suddenly a very large dot moves along, much larger than any I've seen. I judge it to be an absolutely enormous vehicle--one of those monster-trucks used to move construction equipment. Does it appear any different in perception?