He started with 3 stars during first season, he's now 5 stars and going forward 3 weeks later (with a completed new position). Maybe that's something common for a fast trainer, but he's catching up another MC fast trainer (same age, the recommanded guy when you start the tutorial).
that's because a 3* fast trainer gains more than a 5* player.

Are skills randomly allocated after a game or does it depend on the player impact during the game (goals, assists, whatever-u-name-it) ?
random I believe