When I sent a (maybe more, can't tell) PM to JohnM2001 by clicking on the PM button in his profile, it did not show up in my outbox, so I can't tell if I really sent it or not.

It only shows up in your outbox if you check the button under you PM to save a copy for yourself.  It's a little different than the old forum, but it helps to save server space, expecially in the long run.  If you didn't get an error, it was sent.