My beardie gets his bath too but I'm not sure there is much evidence a Cham can be hydrated that way.
A shower is what most here do. Plant in the shower with Cham on it, warm water (not cold or hot) spraying on a wall so it bounces off onto the plant and Cham.
Kath.
He's more than likely puffing up at the tongs or your hand. He's still settling in, he'll eat when he feels ok. Has he plenty of cover, foliage to hide in?
He may not drink in front of you either. Give him time and space.
Kath.
If you've had the UVB 7 months or so, it could need changing. Also I see your basking light is on 24/7. Chameleons need complete dark to sleep properly. This could be contributing to him being sleepy.
Kath.