Magicians are the units that have magical spells but only of a single book. The book school can be defined by several things. It could be special building in the city. It could be researched in magic branch of reseach. It could be simply that the city with particular shard resource produces particular magicians.

Combining (training larger troops) should improve intelligence, while incising veterancy should increase manna/essence and health.

Actually, the unit has to be designed, so in design page, there would be new items - magic books. So that if you give the magic book (of particular school) to the unit, then it could cast spells from that book.

Of course, the name it self is not magician, but whatever you would call the unit when you finish the design.