Does Gilgamesh abuse his authority, if so: in what ways does he abuse his authority ?

Yes, as the story begins, we see that Gilgamesh is a tyrannical leader who shows little regard for his people. He takes what he wants from them and works them to death constructing the walls of Uruk. He sleeps with brides on their wedding night, before their husbands. It is said that no one can resist his power.