Does a submarine pollute the water?

Answer 1

A lot less than the average surface ship of similar size, and certainly not in a manner as harmful.

Modern submarines, like most vessels that are nuclear powered, don't leave behind any fuel oil waste; the only thing that is dumped overboard is waste from the sanitary tanks (fish food - think twice about eating fish) and trash, which is compacted into cans, weighted, and then dumped via a trash tube (essentially the same as a torpedo tube, but smaller and vertical, emptying out the bottom), where is sinks to the bottom of the ocean. Each can must be specifically weighted to ensure it will sink.

Only biodegradable waste products are allowed to be dumped; any materials that don't meet the criteria or are of a harmful nature are brought back to port and disposed of properly. Of course in emergencies, it's a different story, as crew / ship safety takes precedence.