From what I've gathered, there's no jobs in Final Fantasy XII so there are no Green Mages. But if there would be Green Mages, then they would probably use Green Magic (which are not Wind Magic) which contains Shell, Protect, and all the other "buff" spells. (Haste is not included because it's Time Magic, another category of magic in FF XII.)

Also, regarding the summons, the summons that I have seen so far are: Hashmarim, Belias, Altima, Mateus, and Queklain.