I have a bridge that has a crown on each end. The crown near the back has a hole in it. So what I would like to know is can a crown be repaired without damaging the rest of the bridge.

I don't know the answer, but I'd like to suggest that you consider the possibility of getting a dental implant for the missing tooth/teeth.

The crowns are usually porcelin fused to metal and the bridge was made as one piece. I've had temporary crowns fall off, but never permanent ones.

Yes, you can repair a hole in the crown without compromising the integrity of the bridge. You might want to look at the cause though. Is it caused from grinding your teeth?

Yes they can fill it with amalgam if its not too bad... if its very rotten underneath, it will have to be replaced.. also, if it is a hole in a porcelain crown, it will keep chipping... if you don care, don't worry, its just cosmetic if it does not trap food