Welcome to LW! You pose an interesting question.

My initial question is perhaps about the social psychology of the site. Why are two popular subjects here (1) extending lifespan, including cryogenics, (2) increasingly powerful AIs leading to a singularity. Is there an argument that concern for these things is somehow derivable from a Bayesian approach? Or is it more or less an accident that these things are of interest to the people here?

I think there is a purely sociological explanation. LW was started by Eliezer Yudkowsky, who is a transhumanist and an AI researcher very concerned about the singularity, and his writings at Overcoming Bias (the blog from which LW was born by splitting) naturally tended to attract people with the same interests. But as LW grows and attracts more diverse people, I don't see why transhumanism/futurism related topics must necessarily stay at the forefront, though they might (path-dependence effect). I guess time will tell.

Examples of other things that might be of interest could be (a) "may I grow firmer, quieter, warmer" (rough paraphrase of Dag Hammarskjold), (b) I want to make the very best art, (c) economics rules and the key problem is affording enough for everyone. I'm not saying those are better, just that they're different. Are there reasons people here talk about the one set and not the other?

If you have something interesting to say about these topics and the application of rationality to them, by all means do! However, about topic (c) you must bear in mind that there is a community consensus to avoid political discussions, which often translates to severely downvoting any post that maps too closely to an established political/ideological position.