My take on #1. Bran might have known that Daenerys would burn down the city, but what was he supposed to do to stop it? He could try to convince people but they wouldn't be able to stop her anyway. He knew the only one that could get close enough to kill her while she was unprotected was Jon Snow. The only way to convince him that she wasn't fit to be queen was to allow him to see what she had become. I agree no "claim" was necessary for him. He was chosen by the most powerful families left. That's a stronger "claim" than anyone has had, really. Someone could still try to overthrow him, but they would likely face fighting the other 6 kingdoms in the process. His rule is more stable than when various houses were constantly fighting for the throne like before. Yara could try to split with the Iron Isles, but she already agreed to stay as part of the 6 kingdoms. It's not like she was forced into it. Same thing with Dorne.