[Cronos]

These places include Hungary, Estonia and Finland (all of which ended up adopting an Uralic-Altaic language as their own).

Not quite correct -- the Magyar who moved there came BEFORE the Mongols.

[muawiyah]

There were certainly Uralic-Altaic speakers living in what is now Hungary BEFORE the Mongol invasions. However, the Ghengis Khan event was the big one and dwarfed everything that had happened before.

In the end the Germans, Slavs, Latins, and Hungarians, including the Magyars and other Turkish tribes who'd lived there for centuries, adopted the language of the Mongol invaders.

Again, you want to learn Hungarian, attend Indiana University ~ they have a long tradition of teaching it. They are also the only school in North America to teach Sa'ami!