I'm running a wizard with the Air Elemental school.
There are spells with the [air] descriptor, and there are spells on the Air Elemental school list. These are different lists; for example, Lightning Bolt isn't an [air] spell but is on the air school list (in the same way there are acid spells on the Earth list and cold spells on the Water list).
I am pretty sure that the Elemental Focus feat is based on the descriptor; Elemental Focus (air) does not affect Lightning Bolt.
I am almost positive that I can't take Spell Focus for the Air school.
I am less sure about elemental opposition schools. Earth is my opposition school; does this include only spells with the [earth] descriptor, or all the spells on the Earth school list (like acid arrow)? The Elemental school spell lists are so haphazard and only vaguely related to the elements they represent, I am inclined to say that it makes little sense to tie any game mechanics to them as groupings, so base opposition schools on descriptors.
Whaddaya think, sirs?
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You the spells in your opposition school are those explicitly named in the Earth school list. Nothing more, nothing less.
Elemental Focus increases the DC of spells with the relevant descriptor in the spell type. Elemental Focus[acid] would affect any spell with the acid descriptor, regardless of its appearance, or lack of, on any school lists
*My earth school wizard took Spell Focus[Conjuration]. Only a handful of spells for the earth school have the acid descriptor, and most of those do not allow saving throws.