I plan on going to the Galleria as my first visit in Rome, thus it would be free with Roma pass.
When I try to reserve will they require payment with credit card? If so, do they reimburse or should I 're-think my first visit?
No, they will not require a credit card payment. However, the only way to make a reservation using the Roma Pass it to call them. You can not make a reservation using the Roma Pass online.
Or have your hotel call for you. Make sure they know you are using the Rome Pass. Then pay for reservation @ office when you arrive at least 1/2 hour early.
I asked our hotel and they called for me and then they sent me an email