They have Pack-and-play cribs on the ship, nice and clean and in good repair. Ask for one when you make your reservation--call them now since your ressie is already made.
First, don't panic about so much to learn. You will be given all the information again when you get on the ship--in the kid's navigator, the daily adult navigators, etc. It helps to learn in advance, but don't panic over it. I think you'll find that this is a very relaxing vacation from a "mom" standpoint. I think it's far easier than the parks.
Your kids will be in the Oceaneer's Club, and the 3 older ones will be in the same group (built in play mates). The baby will be in Flounder's Reef. When you board, you can go there and make baby sitter appointments. The last I knew, they allowed you to make 2 or 3 reservations initially, then add others on a "space available" basis.
Weather can vary any time, but March should be good. Best advise--pack, then remove at least 1/3 of what you thought you'd need. Do take plenty of diapers and baby supplies as these are available in limited quantities and limited sizes on board.
There are laundry facilities on board (I know you don't want to spend your vacation doing laundry, but it is nice to know that there is that possibility). Dress the kids in play clothes most of the time (including dinners). They're little...just have fun. One fancy dress for formal night...