I agree with pretty much everything there. (GOD! That end fight! RARGH!) But I'll argue the point of her bitchyness towards Zuko. That one I actually felt was justified. I mean he'd convinced her to trust him in Ba Sing Se, and then immediately threw it back in her face, almost getting Aang killed. It was awesome, and it made his character more complex and interesting, but yeah. To her, his bumbling was just a repeat, she'd fallen for it once and the consequences were dire, she wasn't about to fall for it again.
...not to mention her similar experience with Jet, now that I think on it...
But yeah, that one felt pretty natural to me. As a viewer, I was on Zuko's side, but if I put myself in Katara's shoes I would've felt the same. I think it would've been much weirder if she accepted it easily (In fact, I was a bit thrown off that she agreed to go along with one Aang wanted, I expected more of a fight there, so bravo for putting the mission ahead of a personal grievance!)