Private messaging. This can be done with bbpress.
Yes, there is a plugin for this
 Groups. Can this be done?
Not yet (put it on trac as request). There is a way with an plugin I believe. Make a new group (e.g. like moderators) and put your people in it.
 AND THE BIGGEST OF ALL – Can “friends” be made for a member, where you click his/her profile and friends are listed?
I was working on a plugin that does this, but I got stuck with it, so it’s back on the selve for now.
Can’t help you with the other questions