You're right, the 30 gallon is way too small. The gator needs a haul out area where he can get out of the water to dry off as well as bask, so you need to create such an area for him in the larger tank. The basking light should cycle off at night, but the water should remain constant. Feeding mice is recommended at this size. Fish are ok as a supplement as is beef and chicken.
Mice are a pretty good source for the various nutrients that it needs.
It will let you know if it's being fed enough. As to his temperament, it's hard to say. Sometimes extreme stress can have a paralyzing affect on them. When you set up the new tank, give it some areas to hide in, something that will break the line of sight from the rest of the room. This will help it feel less vulnerable.