1. I think he wanted to prove he could take initiative and be successful. He also wanted to "show" Chuck and the rest that he could get more clients and do his job well without "bending" the law.

2. I think Jimmy wanted to look good in Kim's eyes. Kim had already thought that Davis & Main had signed off on the ad (It's not clear whether he told her that they had and she just assumed that they had since the ad had been shot). Jimmy didn't want to risk running the ad by Clifford and then the firm drastically changing it or outright refusing to do it, which could change her opinion of him.