Welcome!

I want to work on the hard questions of philosophy, grue and induction, cognition and consciousness, nominalism v.s. realism, Bayesian epistemology, philosophy of probability and mathematics in general, and even meta-physics, though I would like to positivize the field a bit.

That's a huge amount of philosophy to look at. Might I suggest narrowing your interests down a bit, at least at first? It's very easy to read a little bit of everything, but much harder to contribute something non-trivial to every field.

Lastly, I would like to ask, how does less wrong see itself? I mean what is the general LW opinion of what LW is? Is it a blog? An open source research institute? A philosophical movement? A non-philosophical movement? A self-help movement? I am curious.

It seems to be a little bit of all of those things. Some people here are rabidly anti-philosophy, and so if LW overtly called itself a philosophical movement, those people would probably end up evaporating off. On the other hand, some people would very much like to see the self-help aspects of LW become secondary to the more philosophical or technical aspects. Like everything else, it's a bit hard to pin down to a distinct category.