Is there any good Eastern Philosophy that is not religiously or mystically inclined? I want to get a good grounding in World Philosophy rather than just Western Philosophy, but in my brief research of Eastern Philosophy it seems to turn into theology.

Your request raises an interesting issue. A great deal of philosophy, east and west, has some of what may be called religious inclinations, as does philosophy out of Africa (pre and post-colonial) and the Americas. But that should not deter you if you are uninterested in such an inclination, as the philosophy that has been generated from Hindu, Buddhist and other traditions in India and China (and elsewhere) contain a massive amount of philosophical arguments that can be engaged from a secular perspective. There are multiple Buddhist arguments about the nature of identity, for example, to delight a secular philosopher who is interested in metaphysics. And Moism in China can provide a good focus if your interest is in ethics and utilitarianism. In terms of access to philosophy from around the globe, I recommend the Blackwell Companion dedicated to world philosophy.

I am a junior in high school and am already well into the college process. I would consider myself to be smarter than average, but will not hesitate to admit that I am not of the most elite caliber (some would say I am more 'street smart' than 'book smart'). During the college process I am looking at schools that would be considered tremendous stretches for my academic profile, however, connections I have at these schools may make up for this gap and allow me to coast on in. Should I feel guilty that I am receiving all of this help? What if I really do like the schools that are outside my profile? The whole point is to end up at the best school you possible can, right? Is there a difference between my possible best and the possible best of myself and connections combined?

Interesting situation! The Roman philosopher and statesman Seneca tells us that the most important thing we have is time, and the most important decision we will make in life is how to spend our time and with whom. I suggest that you may want to go to that school which (after you have completed four years) you can look back upon with proper pride (proper pride as opposed to vanity or egoism). Insofar as skills and adventures (intellectual and otherwise) often involve risk-taking and moving against the line of the least resistance (in other words, not taking the easy route), I suspect it would be better to opt for the college or university community that would most challenge you. Where I teach, there is a tremendous (growing) stress on students discovering their vocation. A vocation is not just a job, but a sense of calling or having a goal of pursuing a fulfilling profession. I would recommend finding a college or university which takes vocation seriously.

Is it possible that a person of modest intelligence could learn the whole history of philosophy, in terms of knowing every notable philosopher (from Thales to, say, Rorty), having read a few of their books or at least knowing and being able to expand upon their positions ... or is it simply outside the scope of a person, any less than a genius to have the time to gain such knowledge? It seems to me that there is not more than a couple of hundred such philosophers, and as such could be accomplished, at least superficially. Or is it more efficient to decide outright to miss some philosophers out?

Great question! By the way you pose the question (Thales to Rorty) I assume you mean western philosophy. Yes, I think you can carry out such a project, reading a bit of each of the major philosophers and then relying on a good history as a guide. I would highly recommend Anthony Kenny's multi-volume Oxford University Press books as lively and engaging. Copleston's history of philosophy is perhaps less engaging but it is reliable and a good companion. Speaking of Companions, Blackwell, Oxford, Cambridge, and Routledge each have massive Companion series that would also be helpful in filling out your reading. You might want to set as a goal an overall grasp of the history of philosophy and then dig in to a few areas and thinkers so as to deepen your understanding of philosophy and also to engage more in the practice of philosophy (wrestling with arguments and counter-arguments) in reference to a specific area or philosopher.

Are there any good critical discussions, if not refutations, of communism, especially its philosophical concepts, e.g. theory of knowledge, communist materialism, dialectics etc.?

Probably Karl Popper's work comes the closest. Get his book (I believe in two volumes) on the enemies of a free society. His work was taken seriously by eastern Europeans who were under the authority of the Soviet Union. Popper provided them with an alternative perspective by which to offer a critique of communism. Popper's work is systematic and fair (except in the case of his critique of Plato, which I believe to be based on a partial misreading of Plato) and historical. A book that is less historical but is profoundly anti-collectivism (and thus communism) is Robert Nozick's Anarchy, State, and Utopia. The latter is full of great arguments, colorful examples, and well worth a slow read.