I was always confused by this. A lot of fics have these so called "trust vaults" set up for Harry with limited money, meaning that he can only access them and has to wait until he is of age to access his main vault.

Is this canon? Did the Potters really have something like this? A 11 year old can access his/her main full vault as long as he/she has the key, right?

Speaking of Gringotts keys, let's say if Harry took his key from Hagrid before year 1 or from the Weasleys afterwards. Would the goblins allow this and let Harry access his full main vault without adult supervision and allow him to do whatever with it's contents? Or if Dumbledore or the Weasleys refused to give him his key, could he go directly to the goblins and ask for a new one? Would they give him one? What would Dumbledore say if he knew Harry took back his key? Would he have any legal ground in demanding it back from him or getting the goblins to block him from accessing his vault without adult supervision? And finally, can the ministry intervene in these situations?

TLDR: I'm writing a fic where Harry simply asked the goblin teller in PS to give him his key because it's rightfully his. The goblin did so, since Hagrid wasn't in his right to take it away from him (since the vault is his), but would Dumbledore be, since Harry is underage ?