There was no cure, except for the Nerevarine. Fyr will tell you that all the other patients he tried the cure on died. "If you return to Fyr at a later point in the game, he will tell you that the potion doesn't seem to work on the rest of his cases and that he killed two of his most desperate patients while testing it. Apparently you are an exceptional case, though as you may have found out, the Nerevarine is supposedly protected from this death by prophecy."
Yes, the Nerevarine was. However the messenger was killed before the Nerevarine entered the picture. Since the House quests play out no matter which House the Nerevarine joins, some variation on that quest happens, no matter what.
Um...no. The Great Houses never solve anything in a peaceful manner. Any "treaties" are usually obtained by kidnapping hostages to influence the outcome. http://www.uesp.net/wiki/Lore:Great_Houses
The Great Houses were never in peaceful co-existence.

The Tribunal went mad, Dagoth Ur went even more mad, and if Nerevar had joined them there would have been no Nerevarine to stop them. Also, since Dagoth Ur would still exist, I'm not sure how you think adding one more false god to the Tribunal would have prevented Tiber Septim's conquest of Morrowind.
I don't mean use them right away. Sotha Sil (I think) was the first to suggest keeping them to study. The decision to use them came later. I know I would want to try to figure out what happened. If the Dwemer had achieved apotheosis, throwing the tools away would have doomed all of the Chimer.*