Since "fish" can be both plural and singular without changing form, "clean fish" means to clean multiple fish, while "clean a fish" means to clean a single fish.

Yes that phrase means "clean a single fish". Where as "clean fish" could be any amount more than one.

"Fish" can be singular (a fish), plural (10 fish) or uncountable (I eat fish). When it is uncountable, we mean it as food, ie. the flesh of a fish. Since the spelling and pronunciation doesn't change, I can understand that this may be confusing for learners.