Dometic refrigerator parts are pretty much only available through an RV dealership / parts store. Dometic doesn't sell directly. You'll likely have to order parts like shelves, and its not going to be cheap. You may want to take a second look and determine if you can adequately repair with plastic weld or epoxy.
And, yes, the crisper tray is intentionally designed to allow airflow. The cold air flows downward from the "coldsink" (opposite of a heatsink) at the top rear of the fridge, so you should take some care about how tightly you pack the fridge. Mind you, I usually remove the crisper tray so I can pack in more food and have never had a problem. Just make sure that there are some vertical spaces at the rear of the fridge so the cold air can work its way down.