Each person in a stateroom can be tied to a different credit card. Thus, his KTTW could be tied to his father's credit card. If you charged tips, that would eliminate any portion of his on board expenses (tips, excursions, purchases) being put on your card.
As to check in, make it easy and have both families check in together. Have your ressies linked which would seat you together at dinner. Yes, they could put cash toward his KTTW instead of a credit card if they choose to do so.
Yes, you will get his documents as the docs for the stateroom will arrive together. You would make his reservations. His parents could pay the TA directly for his fare, or could reimburse you--whichever you decide.
The big key is communication and early booking! Do be sure that you know up front exactly what his family is agreeing to pay so that there is no problem at the 61 day point or on board.