I wouldn't say it always happens in questions. You ask Elkéstél? and not Késtél el? It does happen in questions phrased with a question word (what, who, why etc.) since the question word is always the element in emphasis. So it is the same as your case 3. above.In questions (1 both direct and indirect - as in your example), negative sentences (2) and in statements where a particular word/part of a sentence (3) is emphantic the preverb will follow the verb (and written separately from it).
1. In direct questions: Miért késtem el? (Why am/was* I late?) or indirect questions - your sentence.
Yes, consequently it happens in general when the element in emphasis is not the verb itself (not necessarily with a question word). E.g. Mária késett el? Te késtél el? Tegnap késtél el?... It does happen in questions phrased with a question word (what, who, why etc.) since the question word is always the element in emphasis ...
This is yet something else. I remember I learnt about this with “Megyek le a lépcsőn / Lemegyek a lépcsőn”, but I have never known how productive this is. Hmm I guess it's material for another thread (not now - I'm lazy)As to the word order, there is an other thing to be taken in consideration as well. See the following difference:
Elmentem - approximately "I have gone away"
Mentem el - approximately "I was going away"