how long does it take for a new player to adapt to your team?
Depending of adaptation rate (AR). You can see it in player' analysis. It goes from 1 to 20. More close to 20, faster adaptation of the player. For low AR it takes half season, more or less.
Do premium features take into account in team report the adaptation of new player?
Yes it does, like moral, but it doesnt take into account condition (there is a penality under 93%).