I was also able to set it up so a Trainer/Mentor can view and update availability for all of his trainers, but the trainers can only view and update their own schedules

Ans : If you are setting up the trainers as directory profiles, you can assign additional contacts that can access that profile’s scheduler. He can then switch between each profile at /account/menu and can see and edit their schedulers.

When logging in as a member, I was able to book/schedule a training session without purchasing a session. How can we set up the system to avoid this?

I don’t believe we support this. Is there a reason you don’t want them to pay directly vs. buying vouchers? Typically the vouchers would be sold in a bundle for a lower price.