Re: First Doctor - character arc?
He mellows by the end of The Edge of Destruction (serial 3), though he's always a lovable grumpy bastard.
I think The Aztecs is often the episode that's pointed to as the point he mellows out. Certainly, The Edge of Destruction itself resulted in everyone being at each other's throats. Certainly, by the Dalek invasion of Earth, he's affirmatively seeking to be a hero.
When on Romulus, Do as the Romulans