I'm leaving for airport after my round. Can I store bags there while I play? Would be nice to change clothes there and head straight to airport after if possible.

Yup, locker room and shower

Doesn't sound like an unreasonable request. I imagine you might be able to use a locker or 2 in the locker room. I suggest you check with the clubhouse ahead of time just to make sure. Have a good round a safe trip!

Yes & convenient to MCO.