In Keyforge, does an attacked, exhausted creature deal damage to the attacking creature?
Yes, they deal damage back (but they are probably not exhausted in the first place).

The rules you quote do not say anything about the exhausted status of a creature affecting how it fights. Therefore there is no effect. 

That said, cards unexhaust at the end of your turn, not the start. Unless you have cards that allow you to exhaust your opponent's creatures, the creatures you are attacking will be unexhausted.