The anole, also know as polychrotidae, is in the faimly of Iguanidae.

Yes. Sauromalus ater or common Chuckwalla are vertebrates of the family Iguanidae.

Collared lizards are in the family crotaphytidae (Collared and Leopard lizards). They are in the same suborder as the family iguanidae (iguania).

David F. Avery has written:

'Evolution of the iguanine lizards (Sauria, Iguanidae)' -- subject(s): Evolution, Iguanas

Kingdom: Animalia

Phylum: Chordata

Class: Sauropsida

Order: Squamata

Suborder: Iguania

Family: Iguanidae

Genus: Iguana