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.
Start with a large brush to clear the big areas quickly, then switch to a smaller brush for the edges. Use Put it back to restore anything you took away by mistake, and undo to step back through your last dozen strokes.
A plain background that contrasts with the subject is far quicker to work with than a busy one. The result is a PNG with a transparent background. To use it as a passport photo, bring it into Passport photo and pick a white or light blue background there.
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.
The working copy is limited to 1400 pixels on its longest side, so a larger photo is saved at that size. That is plenty for a profile picture or a document photo.