My understanding at this point is that they joined the Axis to avoid getting invaded, then when Russia was at the point of invading them they surrendered, but were forced to keep fighting by the Germans.

The Hungarians were an early, willing joiner to the Axis. Part of the reason for this was that they wanted Transylvania back from the Romanians and thought that with Germany behind them they could achieve that. The were correct and Germany forced this issue on behalf of Hungary. The Hungarians willingly offered up troops for the Invasion of the Soviet Union although they played an inconsequential role.

After Romania capitulated to the Soviet Union and switched sides Germany was afraid that Romania would do the same thing. So, in a famous incident led by Otto Skorzeny Germany deposed the Hungarian ruler (Admiral Horhty) and put in power the fascist Arros Cross party. The Arrow Cross party were fanatical anti-semites and it was after their coming to power that the holocaust started for the Jews of Hungary.

Once the Russians crossed the border into Hungary is when we see a real Hungarian military participation in the war. They fought tenaciously in many major battles including the Lake Balaton offensive, the sieges of Budapest and other actions.

I'm no professor, just a simple university student here in Hungary. My studies cover a fair amount of history, and I've read several books so I have some knowledge.

"Did the Hungarian Upper or lower classes support Nazism?" I'd say that the lower and middle classes supported Hitler but didn't really care much about Nazism. Hungary didn't really enter the war because of a German ultimatum of an attack, they enterred it because of one single reason: Hitler promissed the return of the land taken away by the allies after 1918. You can read more about it here: http://en.wikipedia.org/wiki/Treaty_of_Trianon The result of this treaty was the radicalization of the population. There are still families who have relatives living in neighbouring countries. It explains a lot about the rising extremists here. For the Upper class, I do not have much information. I'm sure that they weren't Nazis, nationalists is more like it.

"Were the Jewish people prosecuted?" Hungary had the first law in Europe against the Jews, right after the first world war. The law set quotas on Jewish entries to the universities. There must have been several laws, but there is one key element. The ruler Miklos Horthy protected the Jews to the final moment, until 1944. That is a big thing. There were no Jews deported from Hungary until that point. In 1944 the Germans abducted Horty's son, to blackmail him to give up his power and after that they started deporting, and killing. There are documents that the rulers even made jews come back to Hungary, before that. Nevertheless they were second hand citizens, and lived in the Ghettos. Recent documents show that Horthy knew about the concentration camps.

For the last question, Hungary enterred the war on Germany's side because Hitler promised the old territories back. That was the biggest reasons. To the end I'd like to add that Hitler did infact give territories to Hungary, he fulfilled his promise. For that we gave the lives of soldiers but no Jews.