I am glad to hear you are excited!
I hadn't considered mentoring the whole team - I think it's probably best to pick one character with whom they have a special relationship to add the extra Trust with. Giving it to everyone seems a little strong. But if you want, you could give them 2 moments with each party member instead.
And yes, the bonus Trust from being a mentor is in addition to the usual +1/-1 that everyone gets.