She is trying to lay eggs. If she is digging, she needs a lay bin immediately. I dont use a full size trash can, just a 10" deep bucket, that is 12" diameter. mix 50/50 clean dirt and sand. I usually damp the soil to make it easier to dig.
Try the rain dome from AquaZamp. The hood goes outside the screen so when it rains, it allows water to collect on the screen. Mine drink this way too. You can get this effect easily by pointing a spray nozzle at the roof of the cage.
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I would go with a quad fixture. I always used the arcadia double fixture from Todd. Once I had an extra fixture, I doubled up and tried it on an enclosure. The four bulbs works much better and penetrates much deeper into the 4 foot enclosure. 2 or 4 arcadias you cannot go wrong if switching from...
Excessive roaming and movement may be a sign that he does not like the conditions. I would also move the light off the top and suspend it maybe 5 inches over the cage. That way if he does climb on the top, there is no chance he can get burned.
Napping and sleeping during the day are a sign of illness. They may close there eyes for a minute but keeping the eyes close is not a good sign. If your friend's cham takes naps, tell him to get on the forums and seek help regarding his husbandry.
For this cham, your temps are way too high...
It looks like a burn. I thought it may be the precursor to a shed but if has been there for a week and a half that is unlikely.
He looks really under weight. I would step up the amount of food you are offering and trash the cubes, those are not a good gutload. I recommend cricket crack or...
If he is under his heat lamp, they turn dark to obsorb heat faster. If he is just hanging out and dark, he may need some more time to settle in. I wouldn't worry if he is eating and drinking