Either fully submerged or in just a couple of inches of water is fine. It might be easier to filter a fully filled tank, because they do produce a lot of waste. But that's up to you. They would honestly be fine in just an inch of water as long as their gills are staying wet and the water parameters are to their requirements. He'll be equally comfortable in either situation, but I keep all mine crawfish in fully submerged tanks. It's just easier to put an HOB filter on the tank and keep the water nice and clean.
As far as his molting schedule, they molt less frequently the older they become. So if your crawfish is already fairly large, then don't worry. If he's still little, then it could be cause for concern. How old would you say he is?