How will the new training affect Special abilities & new roles?

Special abilities and new role trainings will work exactly in the same way as they do now. If you have some special ability or new role in progress, this progress won't be lost, and the player will continue to learn this new ability or role (until it's completed or until you pause it).

Whenever you select new role or new special ability to be trained for a player, all the training benefits for him will go to this new special ability or role, like it happens now. And like now, this doesn't have any effect on the player's average quality, so you can "prevent" a player from increasing his average quality by training new abilities or roles, if for any reason you don't want them to improve (so you will receive Negotiation offers, so it will still be seen by low level managers, etc).