Certainly an agent can charge you a fee for changes or cancellations. Often changes take more time and effort than making a simple original booking. If an airline gives a commission, it is almost always only on the original booking. Airlines rarely pay commissions on changes and change fees. I have been charged by my travel agent for changes.

Not sure about the credit card vs. check. My guess is that the agent wants one form of payment for the change. S/he could probably charge the airline's change fee to your card but might not want to charge his/her fee. So they ask for a check for everything. I don't know.

My guess is if you don't pay they won't do the change so at this point you have little choice.

Moral of the story: ask about change and cancellation policies before booking. I do that as much as possible - flights, hotels, etc.

PS it is against FT rules to cross post in different forums.

PPS Welcome to FT.