1) Under ideal, (and impractical), conditions, the bonded brackets could stay there for a really long time. But it is all to easy to loosen one from biting down on something incorrectly or from an impact to the face. And once one has popped off, its neighbors will start coming off, (within a couple of weeks or even days), because the loose bracket and wire is pushing and pulling on the surrounding brackets incorrectly which shears the glue bond. That’s why the ortho needs to fix any loose brackets right away! Any bands could potentially stay on for much longer though, as they can take a lot more abuse than bonded brackets. If your character has full bands he/she could stay a metal mouth for many years if he/she was reasonably careful, ate the proper foods, and was fastidious about oral hygiene.
2) The teeth would move to the point where the archwire had dictated and then stop. If the person kept using headgear, the upper molars would keep moving backwards. That would end up as a really weird bite as there would be no other forces acting on the other teeth. Same thing with an expander if someone kept cranking it open! Continued use of elastics would also over-push the teeth into less than desirable positions, but since the elastics themselves go bad after a couple of years it would probably not be an issue. Also, stocking up on elastics could be a problem after the fall of Rome! Again, the character would have to be very, very careful about keeping his/her teeth and braces clean or he/she would have major problems with cavities and gum disease.
3) Any glue left behind can easily, (but carefully), be scraped off with whatever is handy. Getting too aggressive with a metal tool could damage the enamel or chip a tooth though. Without any tools at all, the glue would be gone within a couple of weeks from eating and determined picking with a fingernail. Bonded brackets could be gone within first week if the person bit down on something wrong. It is hard to say how long someone could keep bonded brackets in place without regular maintenance from an orthodontist. A mouthful of banded braces could stay put for a long time, if the person was super careful about- you guessed it- hygiene.
4) Bonded brackets can be removed in 10 minutes with a pair of pliers and a mirror but that could also result in damaged enamel and/or chipped teeth if you were not careful. Bands are a bit trickier and usually require the right tools and technique, but someone could do it themselves if they were really determined.
Have fun with your story!
