I am not an expert, and this information may not be 100% correct. Just bear that in mind.
I'm pretty sure the war between the Snow Elves and Nords began when the Elves attacked Sarthaal in an attempt to steal the Eye of Magnus, and Ysgramor and his 500 companions began hunting down the Snow Elves for revenge. (Although most people in the third and fourth eras believe it was simply a war for territory). I don't know the details of that war, but the bit about being fed toxic mushrooms is correct, as far as I know. They were enslaved by the Dwemer for quite some time, but eventually rebelled, and fought against them until the Dwemer disappeared. I'm also fairly sure Falmer does not mean "The Betrayed", and is what they have always called themselves (just like the High Elves call themselves Altmer).
As for the disappearance of the Dwemer, my understanding of it is as follows:
In the First Era, the Heart of Lorkhan was discovered by the Dwemer beneath Red Mountain, and they and the Chimer fought over it. The Dwemer High Priest/Tonal Architect Kagrenac had constructed the tools Sunder and Keening to harness the power of the Heart, as well as the gauntlet Wraithguard to protect the tools' wielder from their power. The Dwemer also constructed a giant robot god, Numidium, which was intended to be powered by the Heart. When it was clear that the Dwemer would be defeated, Kagrenac struck the heart with the tools he created, and the entire Dwemer race vanished. Three of the the Chimer leaders, Almalexia, Vivec, and Sotha Sil, then used the Heart to set themselves up as gods, and the existing gods (specifically Azura) cursed the entire Chimer race, turning them into the Dunmer. What actually happened to the Dwemer is still something of a mystery, but some have speculated their souls were somehow bound to the Numidium (which would later aid the creation of the Septim empire and the Warp in the West).