As far as the reservation is concerned, they are 2 separate reservations--2 separate OBCs, etc.
The answers to your other questions depend on which port you are at and what their Customs and/or Homeland security requires. We've done a couple of B2Bs and each was different.
You do not have to take your luggage off the ship--if you are staying in the same cabin, it can remain in your cabin. If you are changing cabins, GS and the stateroom hosts will take care of moving your luggage to the new cabin. Ours was held at a storage room by GS, but others have reported the room hosts handling it between the two of them. In any event, you will get a letter from GS on the last full day telling you how the transition will be handled.
On one cruise, we were off the ship for about 45 minutes--thru Customs, wait a short while in the terminal, then back on before the terminal opened to incoming guests. On the other cruise (2011) we didn't have to get off at all--we just went to GS at the specified time and got our new KTTW cards.
DCL provided food in the Cove Cafe for adults and the Promenade Lounge for families, beverages at the beverage station. We could swim as soon as the pools had been cleaned.
If you book on line and have difficulty getting the same cabin, book 2 different ones. Then call DCL and ask the CM to find one that will work for both cruises. That way, you get the on line booking credit! Your TA can also do this for you.