What kind of destruction magic will be in ESO we have only seen lightning and fire and both of them seem limited to Templar and Sorcerer skill lines which would be a bummer. Will frost magic be in the game? Also we have seen nothing of enchantment alchemy illusion or alteration will any of those skill trees be in the game?

There will be three types of destruction staffs, one of each element. The other spells are scattered within other skill lines, besides enchantment which is a crafting skill i think. For example, Mages guild tree has some illusion and alterations spells, as well as the Dark MAgic Sorc line.

okay that makes since but what about the destruction and restoration destructions elements seem to be divided between Templar sorcerer and any other mage class if there is one and restoration seems limited to Templar?

Read my post, i just told you, there are restoration staffs and destruction staffs, the destro staffs come in three type, one for fire, one for ice, one for lightning.

Mostly ESO isn't using that terminology, aside from the destruction staff and restoration staff. Dragon Knights have a bunch of fire and rock spells, Sorcerers have lightning, summoning and 'dark magic.' The mage guild tree (as seen in the quake con video) has Soul Trap, mage light, and Fire Rune, plus a meteor spell and 'equilibrium.'

Alchemy is a craft skill, as is enchantment. Nightblades have a couple effects that would fall under various 'traditional' ES magic lines, but they simply aren't organized that way.

Sorcerer: Lightning

Templar: Light

Dragon Knight: Fire/Earth

Nightblade: Shadow

Destruction Staff: Ice/Fire/Lightning

Mages Guild: Fire