He lives and works in Harmugstahl and conducts experiments on Frostbite Spiders using a special serum (as revealed in a research note), infusing them with frost, shock and fire. As evidenced by the shrine in his bedroom, Kornalus is, like many other magicians, a worshiper of Julianos.
Kornalus is a combat mage and uses fire/frost/shock spells. At higher levels, he might also be immune to shock/fire/frost damage. During the fight, he fights alone. The spiders in the last room are sealed behind bars. However, the Dragonborn can free the spiders via a nearby lever, and they will then aid the Dragonborn in the fight. Once Kornalus is killed, any spiders that are still alive will then attack the Dragonborn.