In LEGO mindstorms NXT programming: is it possible to download a file from a robot onto the computer?
Yes, you can download it back in computer. But you can't work on it anymore - it is already compiled (has .rxe extension). However you can download it on another NXT and continue to use there. You can edit and work only with .rbt files. 



My LEGO MINDSTORMS NXT program doesn't work anymore for already two months... Some problems with flash player. So I can't provide any screenshots.