No clothes in the judging ring but you use them will benched, some show halls do get really cold.
I personally don't use a cat bed in my sturdis, the cats don't like them. Instead they prefer to use extra liner sheets.
As for the CFA mentor program - I never used the program so I don't really know how long it takes to get one.
If you'd like, pm me exactly where you are and maybe I can find you a mentor in the area as well
I know a few excellent breeders in CA, I can put in a good word and see if they are willing to help a friend of a friend!