I just finished working with a personal trainer, so I might be able to answer some of your questions.
Now, I got her through my gym; she is their employee. So I didn't pay her directly. I didn't tip her either. However, we did meet once a week, on a schedule that worked well for both of us.
It was a package deal: 4 sessions, once a week. She was great!
Good luck with getting more answers...
I expect to pass through this world but once; any good thing therefore that I can do, or any kindness that I can show to any fellow creatures, let me do it now; let me not defer or neglect it, for I shall not pass this way again. Stephan Grellet