There was also The War Games where the Time Lord tribunal were going to give the Doctor the choice over what his next form would look like, but he took too long so they made the choice for him. Some think one of the options resembles Peter Davison.
The first episode with Ashildr in season 9 rather awkwardly hamfists in the explanation that the Peter Capaldi form comes from the Doctor subconsciously remembering Fires of Pompeii during his regeneration, complete with a five minute clip from Fires of Pompeii with Donna pleading to the Doctor to save someone and the Doctor ultimately going back to save Capaldi's character and his family. Apparently, taking on a form similar to the man he saved is supposed to motivate the Doctor to save people wherever possible.
Like I said, awkward and hamfisted.
Yes.