Definitely not. There are lots of mixed marriages of different kinds: Hungarian man with foreign wife or vica versa, and the parties can be both from the Eastern or Western world. Nowadays around 10...
no, it is impossible... you can only get it, if you take a Hungarian language exam, a Hungarian history exam and you live a lot in Hungary and after if you've got all, you can request Hungarian...
It depends on each company as to who they employ. Generally though if the company can afford an outsider, they will, providing the dancer is very good.