"How did it happen?" is accepted now. I can't speak for the Italian, but in English "How was it happening?" and "How did it happen?" are very similar (native English speaker).
I'm not a native speaker, but I would translate your sentence as "Com'e' successo?"
Pretty sure in english we would use 'how did it happen' for both imperfect and perfect translations
I can tell you weren't around in the 70's, LOL! Everything and everyone was "happening" back then!
But there is this 'quirky' thing with English ... 'used to' (usually in past tense) does not exist as an infinitive or present tense. It has to be rewritten with the adverb 'usually', or in some other way.
"used to" is a habit, and does not go well with "happen" that usually is a sudden thing (seldom repeated). Further more, since it is a question, and has to be constructed with 'did', did is never followed by a conjugated verb, but only infinitiv. So if it was something repeated, the construction would be: How didt it usually happen?