We've had them come off in one piece and we've had them come off in several little pieces. Mostly several little pieces.

A razor blade or scraper is useful to pry the little bits off. To get the glue off I use a DA air sander. Aircraft stripper will work too if you don't have tools or a compressor. I wouldn't use this if you are trying to save the paint on the rest of the car, though.

We've never had a problem with a severely rusted top that was under vinyl but I know of several guys that have. At worst we've found surface rust that we ground off.