The Dwemer's disappearance is unknown, even the scholars that delicate their life to find out what happened to the Dwemer still do not know. The best answer is the Dwemer attempted to play god and got turned to dust.
Yes but that is their mortal forms. All mortals on Nirn have an afterlife, decided by either their race or their actions and dedications in life. The souls of the dwemer are *somewhere*. The question is, where?
During the battle the Chimer and the Dwemer generals (Cant remember names) began to fight. Before the meltdown of the treaty both generals grew friendships but it fell apart after a Dwemer priest discovers a way to tap into the Heart of Lorkan (Dead god) and reach "full enlightement" and the Chimer did not like this. Snapping back to the battle and the Dwemer general is struck down and in a moment of distress the priest uses Sunder and Keening to tap into the Heart of Lorkan and the Dwemer just go *POOF*.