Are the same proficiency cards chosen in game 6 to be used in game 7, or can the Heroes choose new ones?
There is no campaign mode in the game. It is game that has seven different setups/rulesets. There is nothing you preventing you from changing your character between games.
The rules for both 6 and 7 are silent on this and, in fact, only the picture in the rules for 7 is the only way to tell they are even to be used in game 7.
Everything in the game is cumulative from previous years. You didn't remove year to cards from the Hogwarts deck when you got to year three did you? Same thing applies here.