Hey! Thanks so much!
Thanks for bringing this up— these are all known issues, I just ran a kiosk at a con personally.
The dpad/analog controller rebind issue is one we've fixed internally, and I just need to release the update. Should happen in the next day or two.
The game currently saves bindings by controller, and it persists until you close the game. Resolution settings Should save and reapply when you reboot the game, I think? The resolution will update after the Godot splash screen.
The stick vs pad thing was a placeholder setting we had before proper controller rebinding was added in 1.1.0. It didn't do anything that isn't possible with the new menu.