That's exactly how i remembered it

They didn't, Zaheer is not Amon, he is a powerful criminal with a clear goal, which we don't know, gaining support may have not helped him at all. He just went to the Air temple because he tough he would find the Avatar with the rest of the Air-benders, he was wrong so he retreated, he did get the medallion. Also does nobody cares that he is an instant expert, while everybody else is training to be air bender