The dwemer mysteriously disappeared after tapping into the Heart of Lorkhan. When Bamz-Amschend, a dwarven city was discovered, it consisted of piles of ash near armour, weapons, chairs, tables etc. Does this suggest all dwarves were reduced to ash when the power of the Heart was tapped into? Or is the fact that the heart was tapped into resulting into the dwarves disappearing only a theory? What are some theories as to what caused the dwarves to disappear and if so where are they after disappearing?

I think the piles of ash just proved they were chain smokers

Makes sense... Or they just all walked into their stupidly annoying fire traps.
But seriously...

http://www.imperial-library.info/content/definitive-guide-dwemermay be a good start.

There is also the http://www.imperial-library.info/content/final-report-trebonius, which addresses the specific issue.

As a brief summary, there are several hypotheses about what happened to the Dwemer.

A; Kagrenac used the tools, attempting to elevate the Dwemer (or maybe just himself) to godhood through the Numidium. This consumed the entire Dwemer race (likely through the link of The Calling) to fuel the apotheosis, though they fell short (IE didn't have enough collective power) and only achieved a half-state. They became the Golden Skin of the Numidium. (Supported by the Final Report, and circumstantially by Arniel's Endevour in Skyrim)

B; Kagrenac used the tools, and it backfired, totally obliterating the Dwemer (one outcome proposed by the Egg of Time)

C; Kagrenac used the tools, and it backfired, transporting the Dwemer into some distant Outer Realm (another outcome proposed by the Egg of time, supported by Yagrum Bagarn, and circumstantially supported by some claims in The Infernal City)

D; They were hunted down and slaughtered (highly unlikely, with no real supporting evidence)

E; They were stolen away by Azura as punishment not only for the Numidium, but also several other minor transgressions against the Daedra (I've never actually seen any support of this)

F; Some or even all of the above. Alot of the conflicting stories around the Battle of Red Mountain, along with the involvement of the Numidium, indicate there may have been a Dragon Break involved. If so, it was an absurdly messy one apparently ignored entirely by the Jill's.