1. Vienna is, relatively speaking, a major prize both in terms of prestige and in its role as one of the core commercial centers for the Danubian trade (and one of the main routes into the southern German markets). While one could very easily make the argument that, logistically speaking, holding the city with an army based in Constantinople would be next to impossible, I can't see them just withdrawing. I imagine Lower Austria, at the very least, would either be given to some major Magyar nobility to help buy the Hungarians into their new position as an Ottoman vassal, or at the very least be forced into a more enforced tributary situation to the Sultan. In the later case, the tribute alongside surrendering all claims to the Crown of St. Stephen, alongside other political concessions (A crack-down on March warfare and a free hand to deal with the Venetians, for instance) would be part of returning the city to Austrian control. Thanks to its geography, however, I can't see it completely losing its political-economic significance
2. Vassaldom for Hungary was a lot less of a political headache than annexing it directly. Islamization (Or at least Protestantization) would probably have been a tad stronger, and the relationship with the center tighter given the Magyars have no other major power broker to turn to to help enforce their autonomy, but its too far away from Constantinople to be worth the headache.
3. Protestantism probably gets an early boost, as the "decadence" of Catholicism is cast as the reason God is abandoning the continent to the Heathen. The Hapsburg prestige (in Austria at least) also takes a pretty big knock... likely losing their monopoly on the position of HRE and, therefore, leaving the nation more decenteralized and the minor principalities more able to persue their own interests without having to worry about Imperial intervention or contributing to the common Imperial defense.