I think Joseph II made a mistake when when he abandoned Latin as the common administrative language of the Holy Roman Empire in the 1780s. One common language that didn't discriminate against any ethnic group would've avoided some of the later problems, especially with Hungarian being so difficult, and the Hungarians using it as a weapon against minorities in the areas dominated by Hungary.
(I believe though Latin was still used in the Hungarian part until the 1840s.)
the amount of stuff I don't know is huge -- the amount of stuff I don't know about history specifically is also large.
About the Austro-Hungarian split, from what I've read it's not only the language (have you heard hungarian? it sounds like nothing on this planet!), but also that other minorities were not given a chance to get their own kingdoms in the empire
There are some online Hungarian language courses — would you like links to them?