- Is there a "feature request triage team"?
No, there is a product manager for the public platform Q/A.
I suspect several sources, in any order: Vision and Goals as set by upper management, the product roadmap, market research, internal feature list (Is the Trello board still on?), surveys, user research, competition, suggestions posted on Meta.
- Does a more recent feature request get more prominence?
I don't think so although they might be a better fit as those FRs took current features into account.
- Do more votes make a feature more likely to be considered?
SE is not bound to the votes so they could still implement an unpopular FR. I imagine it re-enforces the decision to put an FR into the build track if Meta has voted favorable for a feature.
- Is a feature request ignored if it has an "answer"? (even if it's not "accepted"?)
No, at least I'm told that this certainly isn't true for bugs so I assume the same goes for feature requests. Only a status tag (not being status-review) puts it out of scope for the internal tooling.