One of our classmate's guests will be the DJ for the reunion. We want to offer him free admission, which is easy if she pays by check. But if she wants to put her ticket on credit card, is there something we should have her do when she registers?

My only suggestion for this scenario would be to set up a place for the member to pay for their registration via a donation in the system and then have you as the admin go to the Event Planner and register the classmate using the Register A Classmate function. You would then be able to select Comped for both registrations since he technically paid via a donation.

What if she pays for both (so they're both registered) and you just reimburse her for one person....

We have the ability for the admin to comp a member built in. The part that we do not assume is that the admin would register someone and use a credit card to do so and therefore that is the curve-ball in this scenario.