To address 2) specifically, I would say that philosophical "Rationalists" are a wider group but they would generally include the kind of philosophical views that most people on e.g. LW hold, or at least they include a pathway to reaching those view.
See the philsophers listed in the wikipedia article for example:
Pythagoras -- foundation for mathematical inquiry into the world and mathematical formalism creating in general
Plato -- foundation for "modern" reasoning and logic in general, with a lot of ***s
Aristotle -- (outdated) foundation for observing the world and creating theories and taxonomies. The fact that he's mostly "wrong" about everything and the "wrongness" is obvious also gets you 1/2 of the way to understand Kuhn
René Descartes -- "questioning" more fundamental assumptions that e.g. Socrates would have had problems seeing as assumptions. Also foundational for modern mathematics.
Baruch Spinoza -- I don't feel like I can summarize why reading "Spinoza" leads one to the LW-brand of rationalism. I think it boils down to this obsession with internal consistency and his obsession to burn any bridge for the sake of reaching a "correct" conclusion.
Gottfried Leibniz -- I mean, personally, I hate this guys. But it seems to me that the interpretations of physics that I've seen around here, and also those that important people in the community (e.g. Eliezer and Scott) use are heavily influenced by this work. Also arguably one of the earliest people to build computers and think about them so there's that.
Immanuel Kant -- Arguably introduced the Game Theoretical view to the world. Also helped correcting/disproving a lot of biased reasoning in philosophy that leads to e.g. arguments for the existence of good based on linguistic quirks.
I think, at least in regards to philosophy until Kant, if one were to read philosophy following this exact chain of philosopher, they would basically have a very strong base from which to approach/develop rationalist thought as seemingly espoused by LW.
So in that sense, the term "Rationalist" seems well fitting if wanting to describe "The general philosophical direction" most people here are coming from.
+1 for "Lesswrongers" or "the LessWrong community"
A name for an emergent community is going to have to also be, well, emergent. But you can nudge that emergence in the direction you choose. I think LessWronger is the next natural candidate. I was introduced to a group once as a "LessWronger" even though today is my first time posting or upvoting anything here despite being an avid SSCer for 3 years. I've always been aware of LW, and the label would have been OK for me.