Bear in mind it's Polish from Enlish and the best way to translate "What is happening" is "Co się dzieje". But of course, "co się dieje" is just as good translation of "What's going on".
It all depends on the context.
Hmmm... "dziać się" sounds more continuous to me, and "zdarzać się" more about one-off things? I think "zdarzać się" isn't common in Present Tense, but it surely works in sentences like "To się czasem zdarza" (This happens sometimes) and similar.