Many decades ago, something very close to your question seems to have motivated philosophy professor Paul Arthur Schilpp to launch the multi-volume Library of Living Philosophers, which now contains more than 30 volumes. You can find out more at this link. I seem to recall reading an editor's introduction by Schilpp that explains in detail his motivation for launching the series. You might search for it.
"Philosophy" is derived from the Greek for "love" and "wisdom" and it is often rendered as "the love of wisdom." So one reply to your question is that the proper object of philosophical inquiry is whatever is a fitting object of study in the practice of loving wisdom. So, historically, those recognized as "philosophers" have investigated the nature of reality (Ancient Greek philosophy included theories that anticipated the atomic theory of matter and evolution...), human nature, values (including ethics, accounts of beauty and ugliness good and evil), our capacities to know ourselves and the world, reflection on logic, perception, memory, the sacred (is there a God or divine or sacred reality such as the Tao), questions of social values, matters of governance (political philosophy), and so on. Arguably, the quest to live wisely (or in light of loving wisdom) involves seeking insights into a very broad array of topics that are difficult to limit.
Sometimes historical events can shape the way philosophers work and what they work on (and see as the "proper object" of philosophy). So, in the 1950s and early 60s, philosophers in the English-speaking world largely neglected applied, practical ethical matters (the exception being those philosophers who were engaged in the Civil Rights movement in the USA), but in the midst of the Viet Nam War in the late 60s, and beginning in the early 1970s, philosophers gave far more attention to applied ethics (just war theory at first, but then ethics in medicine and a growing number of other domains).
During some periods in the history of ideas, groups or movements of philosophy develop that seek to pronounce and enforce an idea of what kind of philosophy is "proper" or improper. At one time or another, some philosophers have sought to determine (and sometimes even prove) that at least one of the following mix of philosophical convictions or methods or domains are improper:
Philosophy of Religion
The History of Philosophy
I believe that none of the above have been "proven" to be improper or sterile or out-of-bounds, and I suggest that when philosophers claim things like "X is dead" when X may stand for Metaphysics or Foundationalism or Skepticism (etc, etc) it seems less than obvious that the "philosopher" is a lover of wisdom.
In the full sense of the word this question is unanswerable. I don’t know a serious educated person who does not worry about it. On the one hand, if you do not read philosophers in the right order you are bound to miss the significance of something the later person says. I’m not saying you run the risk of missing that significance; you are guaranteed to do so.
And yet this is a half-truth, because there is plenty you will miss if you start back at the beginning of philosophy and proceed to the end. First of all there’s the obvious problem of motivation that your question implies. If you have to read Descartes before Kant, and Aristotle before Descartes, and so on, you will have been lost or sidetracked before you ever reached the people like Nietzsche and Kierkegaard who first drew your attention. Demanding a strict chronological reading list is impractical.
There’s another kind of problem that affects even industrious people who are incapable of being bored or sidetracked. In many cases we don’t see the full significance of an earlier thinker until we encounter a later thinker. This is what makes some of the later people so important as philosophers, that they bring a new dimension and a new kind of interpretation to what their precursors had said. A passage in Plato on the coldness of ice means more after we read Aristotle on essential predication. Spinoza’s critique of negative emotions becomes livelier and psychologically more significant in light of the way Nietzsche develops the same points. In some ways you learn more about each philosopher by reading the chronology in reverse.
Well, no one can read through the history of philosophy in both directions at once. A general chronological approach, guided by a good teacher, is the best place to start. You acquire a sense of the history of philosophy as a whole and then read on your own to fill in the details. But if you are approaching this entirely on your own, I suggest you start with the philosophers who pique your curiosity. If you are inquisitive at all, you will go from them to their predecessors wanting to know more about why they say what they do. Eventually you’ll see that you need to have a sense of every philosopher on the list; and although Kant might seem like just words on the page if you begin with him, the day will come (after Nietzsche and Schopenhauer) when the Critique of Pure Reason reads like a page-turner, now that you see what its implications will turn out to be.
or for another kind of response, you might still ask why many/most philosophers don't publish philosophies of life. You'd have to do an empirical survey there, but i'm guessing that for many, a philosophy of life is too big and hard to construct. Much easier to focus on some relatively narrow problem and work out a sophisticated view on it ... And I bet that professionally the incentive is to do the same. A "philosophy of life" is something that aims to the wider market, the general public, but the professional incentive is to impress the professional philosophers rather than the public. (Alternatively, perhaps many professional philosophers feel pretty confident that the main value in life, at least for them, is the very professing of philosophy -- so they are acting out their philosophy of life even without publishing their philosophy of life ....)
I have to say I think about nothing all the time, both in the sense of not thinking about anything, and in the sense of contemplating the concept nothing. P.L. Heath has a very fine piece on "Nothing" in the Encyclopedia of Philosophy.
On the other hand I suspect that śūnyatā is not really emptiness or literally nothing - śūnyatā is a kind of non-substantiality, certainly, but in Western metaphysics that does not mean a non-entity. The point is that śūnyatā is emptiness, but of the detritus of external influence, or void or outside dependence. It has its own quality. It is also like a kind of expectant fulness, empty as the rich expectation of a joyous future event is in an obvious sense empty (of the event) compared with the experience of the event itself. A quality however is an entity, though not a substance.
I'm not sure that the outcome of analysing arguments is always that no one is any wiser concerning the issue at stake. And that's because there are several possible results of such analysis, all of which would seem to help us better understand the issue at stake and the justifiability of possible answers: (1) Perhaps the (implicit or not) argument the person offers for her answer is invalid; in that case, the philosopher is able to show that, whether or not her answer is right, her argument doesn't give us reason to accept that answer as right. (2) Perhaps there are assumptions the person makes in offering her answer but that she doesn't defend; in that case, particularly if the assumptions seem questionable/controversial themselves, the philosopher is able to show that the answer requires more defense than the person has offered. Or (3), perhaps the way the person has framed the question closes off certain possible avenues of thinking about the issue; in that case, the philosopher is able to point out that, since there may be different ways to frame the question, the choice of a certain frame may itself require defense.
All of this is to say that wisdom isn't confined to knowing the right answers to certain questions. It seems also to include an awareness of when you don't quite have the right answer or when you aren't yet justified in thinking that your answer is right.
Well, I think your plans sound great. But of course I would, since I helped develop the Neurophilosophy Track in the MA program in philosophy at Georgia State University (www.gsu.edu/philosophy). I'm not just advertising! (though you might consider our program.) I'm suggesting that your view of philosophy of mind as continuous with the cognitive sciences is a prominent one (and the right one to boot!). Many PhD programs in philosophy (including MIT, but also Washington University's PNP program, UC San Diego, CUNY, Pitt HPS, Indiana, and others) have people and programs focusing on empirically-informed philosophy of mind. Most of them would appreciate your taking some time to study neuroscience or other cognitive sciences. Most of them would allow you to pursue such courses while doing your PhD in philosophy (and some have certificates in cog sci). So, go get an MSc in neuroscience and/or apply for MA or PhD programs that would allow you to get some rigorous training in the relevant sciences. And then join the wave of researchers in philosophy and some of the relevant sciences who see our fields as a joint project aimed at figuring out how the most complex thing in the universe (the brain) does all the remarkable stuff our minds do.
You ask an interesting question. If Philosophy was nothing more than deductive logic, then someone with skills in deductive logic but developmental issues elsewhere would probably excel in philosophy. But most people think that Philosophy involves more than deductive logic--it involves the exercise of "good judgment" which in fact we do not understand very well. Good judgment may or may not be absent of emotion: the philosopher David Hume puts emotion front and center in his ethical theories.
We have a very poor understanding of autism spectrum disorders (indeed the diagnostic category of Asperger's has recently been removed from the DSM). It used to be thought that people with autism lacked emotion; that is generally speaking not true (although the emotions may be different from those of neurotypicals).
On rereading your question, perhaps you see a correspondence between some philosophers' apparent detachment and some autistic behavior. There may be an overlap here but I doubt that it goes very deep (that is, I doubt that a shortcut to doing philosophy is to have your autistic friend do it).
To answer your last question first: I don't regard philosophical inquiry as a game. On the contrary, it may well be the most intellectually serious form of inquiry there is. What philosophical inquiry amounts to is itself a matter of philosophical controversy, but I'm inclined to say that philosophical inquiry consists in thinking as carefully as we can about the most general and most fundamental questions we can ask.
To your other questions:
1. The definition of "knowledge" -- more accurately, the analysis of the concept of knowledge -- has been an energetically disputed topic in philosophy for more than 50 years. Some philosophers defend a version of the "true, justified belief" analysis, with "justified" understood in a variety of ways. Others defend an analysis that doesn't require anything they're prepared to call "justification." Still others think that it's a mistake to try analyzing the concept of knowledge into "more basic" concepts. You'll find much useful information about all of this in the SEP entry on the analysis of knowledge, available at this link.
2. I don't believe that Descartes meant his "I think; therefore, I am" to be a definition of existence. Instead, it's supposed to be an indubitable piece of reasoning, or else an indubitable unitary thought, rather than a definition of a term or an analysis of a concept. Notice, by contrast, that "I am; therefore, I think" doesn't seem indubitable: at any rate, it's not valid reasoning, since it's possible for a person to exist (in a coma, perhaps) and not be thinking.