All really great questions, which, of course, haven't come up in the story yet, so there's no way to know.

I've never been able to completely buy the idea of Harry or most other characters leaving the wizarding world. In fact, I think Harry would be one of the least likely to do so, even among characters who were born into the wizarding world and have no Muggle connections at all. He committed himself heart and soul the day he learned there was a magical world and that he was a part of it. I don't think he could break away, even if given a lot of reasons to. He might want to, or even try to, but he wouldn't be able to do it, in the end. That's not to say I don't enjoy fics where Harry is betrayed or sent to Azkaban and subsequently tells the whole wizarding world to go to hell.

In this story, presumably Snape, as Harry Potter's guardian, has access to the Potter vault, since Snape tells Harry that he now "owns" it, which is a pretty strong statement. We don't have a lot of detail about how the system works, so we have to trust Snape's statement for now, since Harry is such a limiting point of view. The banking system might be no more fair and balanced than other magical systems (like the justice system, which sends someone to Azkaban for life with no trial). This is the same system that allows an escaped convict to access his vault; the goblins apparently do not care what issues the Ministry has with the vault owners. It's possible that Harry's actions against the Ministry (or even leaving the wizarding world, changing his identity, etc.) would have no effect on his ability to continue to use Gringotts as usual, because to the goblins those changes would be irrelevant. Also, presumably not being James' son would not change Harry's right to access the Potter vault, since presumably (in absense of evidence to the contrary) there are no other Potters and James and Lily shared equal rights to the vault because they were married. Harry, even if he turned out not to be a Potter, should still have full rights to the fortune because after James' death it would have passed to Lily in full, and then after her death to her child regardless of the child's relation to James. But for now we really don't know, since it hasn't come up in the story.

I think it would be a lousy Severitus response if Harry rejected Snape at the end. In the middle, sure, but to end the story on that? It wouldn't really be worth bothering to write, if it were going to end like that. Besides, readers would riot.