Automatic background removers guess, and they guess worst exactly where it matters, around hair, edges and anything thin.
An automatic tool has to decide what the subject is. When the background is a similar colour, or the edges are soft, it takes a guess and you are left correcting it.
Doing it by hand is slower for a simple shape and faster for a difficult one, because you never have to undo someone else's mistake.
It saves as PNG, which is the only common format that keeps transparency. Saving as JPG would fill the erased area with white.
Yes. Tick the restore option and paint it back in.
It is the format that keeps see through areas. JPG cannot.
No, which is the point. Automatic removers work by sending your picture to a server.