He should have been? He was part of the Order of the Phoenix. His actions following all of that reveal really demonstrated why he wasn't cut out for that organization. They needed covert and level headed Wizards. Sirius Black failed that.
Yeah, sorry, no. I still don't agree. Sirius made a promise to James to protect Harry and Sirius should have been focused on that. He knew Albus was seeking Harry out. Hagrid told him. That should have been his priority. I have no sympathy for Sirius Black.
I'll give you a concession on the crazy argument for post Azkaban and redirect that Remus should have intervened upon seeing Peter on the map.
Not disagreeing there. Albus Dumbledore is the worst character in the entire series. But we know that as viewers but Sirius didn't. It was pretty well known that they trusted Albus but he didn't trust him when he should have.