Get him off the calci-sand. The particles in the calci sand are actually too large to be dissolved in the lizard's stomach so they kind of sit around in the digestive tract and clump together. If these clumps get too large to pass, your lizard will die of impaction without surgical intervention. Regular sand would be better than calci sand. I use repti-bark for my als. Here's a link with more info on calci sand: http://www.pythons.com/calcium.html
Until you get the mites under control, it would be best to stick with something like paper towels for a substrate. This way you can replace it daily. I'd also keep him in the small tank (easier to clean) until you get the mite infection taken care of. To get rid of mites and eggs that are lurking in the tank and furnishings, the tank and everything in it needs to be thoroughly cleaned every day or two. Once you go two weeks without finding any mites, you can set him up in something more permanent.
The runny poos and agitation could be side effects of a bad mite infestation. Mites are very uncomforatble and can build up very quickly in captivity and if not caught and treated, the lizard will actually die of blood loss.
A 10 gallon tank would be the minimum size I'd recommend for a long term home, but a 20 gallon would be even better if you can swing it. Sometimes it takes them awhile to realize what a water bowl is for. In the wild, since it's dry in your area, your al was probably used to drinking dew drops in the morning. Spraying the tank once a day should provide him with a water source he recognizes until he figures out what the bowl is for.
In terms of food, crickets are the best staple. Make sure you gut load them by feeding them something nutritious for a few hours before offering them to your lizard. I feed my crickets fish food, or a crushed high quality dog or cat food with a slice of orange or a carrot for water. It is also imporatnt to dust the crickets with a calcium supplement that does not contain phosperus (calcium phosphate etc.). Alligator lizards are very prone to metabolic bone disease, so this is very important. I use Reptical with vitamin D3 for my guys.
Good luck with your guy,
Alice