oh, I’ve talked about this a lot! And I actually asked Matt Burnett, one of the writers, if Gems have heartbeats. His answer was “Not naturally, no. The Gems are not biological in any way. But if they wanted to make themselves a heart with their shapeshifting abilities, then sure!”, so no they don’t have a heartbeat because they don’t have hearts. They could give themselves some but I doubt they walk around with them (if Pearl finds the sensation of food moving through her body unbearable I can’t imagine she could handle blood constantly flowing around her body). I once had a discussion about if the Gems shapeshifted themselves hearts for Steven’s sake (so he wouldn’t be unsettled by them not having heartbeats) and it also included a discussion about a sort of Gem version of heartbeats, a melodic pulse from their gem from the energy output (you can read the old discussion here)
The blushing I believe to be superficial, something like a social cue/emotional reaction without the biological process that causes a human blush. Just what the emotional meaning behind it is triggering a change in their physical projection. (this is pretty much how Lauren Zuke, one of the storyboarders, describes it too)
As for if they’re warm or cold, that’s also been asked too. During the AMA someone asked if Gems have soft and warm skin like humans and Rebecca said “They can if they want to!”, so its really up to the individual Gem. Naturally they’re probably pretty hard, since they are magic rock people afterall. But I think our main 3 would have something closer to actual human-like skin, due to their exposure to humanity and being around Steven. I have an old post with my headcanons there, if your’e interested. You can read that here (and here, for the ‘homeworld’ Gems)