Does Rumplestilskin knows that he really is a fairytale character?

Yes, he does. This was revealed in the episode "skin deep" when he was in jail and Regina made him say his name before she would give him the cup that he wanted.

This may sound confusing. I think he remembers who he was. But not as a fairytale character. He remembers his life from the other reality.
He realizes that the curse is breaking and is trying to grab power. Under the curse nobody aged.
Now that time has begun to move, he knows he needs to regain his power because he is mortal.