originally film cameras used a reflector to bounce an image onto film, which was light sensitive and would capture the reflected light as an image. This however has changed a lot over time, with them now using digital light sensors instead of film, which has in most cases eliminated the need for the mirror.

also as well as what others have already said, some space craft often orbit in geosynchronous orbit, which means they hold position above the earth by moving at the same speed as the rotation, so if you and the earth are rotating at the same relative speed it will look like it's not moving