It is lovely that you have bought him a Silent spinner and some toys, he will love them
I have just cleaned him out and his wooden toys are drying out (they smelt really bad of wee but I didn't realise this last week until I had already cleaned his cage - his last owner never bothered with pet disinfectant or anything). He is currently slurping on some rice pud baby food
I think he will be fine with moving cages, he didn't seem at all bothered by coming to live here
I'm not sure about climbing, but he can jump when he wants to but not very far upwards so I don't know what to recommend to be honest