You've made it repeatedly clear that you can't stand most, if not all, Marvel movies so I'm not sure why you're even in this conversation in the first place tbh.
Yeah, that part is problematic. My take - is much like yours. I've read compelling arguments that he went into the past because it was always going to happen, but that calls into question, for me, all the other time travel moments in the film. So I see it like you do, it had to be an alternate timeline created when he chose to stay in the past with Peggy. One thing that supports this is that he has a shield to give to Sam. This also suggests that he did Capt America stuff in the alternate timeline.
What breaks things for me is that I feel like he should have returned on the time travel pad. I've since heard an explanation that if in the alternate timeline he still did the superhero thing, it's simple enough to assume that alternate timeline also had its assortment of geniuses, one of which could have sorted out how to get him back to the main timeline. I suppose that's possible, but I think perhaps a bit more explanation around the entire scene would have been good.
Stark didn't refute it and Endgame isn't Inception. The movie isn't out to trick you or make you ponder it's ending forever. From a meta perspective, the audience should assume Hulk is accurately laying out the rules of time travel, barring notable evidence to suggest he's got it wrong.
Well... it isn't the exact same way. Everyone else returns on the platform of the time machine. He just appears on the bench. This is on one hand a small detail, on the other, it introduces the big question about wtf Steve actually did.
Not necessarily... Since they did not get the space stone from that time jump, it's a little unclear if that whole divergent timeline got snipped by returning just the mind stone.
If she still exists, its because she no longer exists in her alternate timeline but rather the main timeline. We have no reason to assume that someone who moves to a different timeline winks out of existence when their original timeline ends.
See above. You are presuming too much and then turning it into justification to be condescending. Chill.