I am on a smaller server but I'm seeing delays from the big servers, yeah. I'm trying to advocate for people to find smaller servers (e.g. < 10k users) but it's something that really needs improving in the UX (that is, encouraging people to use smaller servers instead of joining one big server. I try to recommend https://fediverse.party or https://joinfediverse.com).
As with sibling, it's possible but it hasn't happened in any way that bothers me. Seems like it's just CAP theory in action. I don't think consistency is the corner of that triangle to optimize for in this case.
Presumably? Short of coordinating with someone to check I'm not sure how I'd even notice.
(I'm a different person than who you replied to, but have had the same experience, the instance I'm on is perfectly responsive)