Learn Italian: Dove abiti ora? - Where do you live now?

Usually, yes! Just like in English, question words like dove (where), chi (who), and che cosa (what) are placed at the very beginning of the question to show what information you are looking for.

Where is the word for "do" in the Italian sentence?

Italian doesn't use "helper" verbs like "do" or "does" to form questions. While in English we say "Where do you live?", in Italian you simply ask "Where live you?" (Dove abiti?). Your tone of voice going up at the end of the sentence is all you need to show it's a question.

Why isn't there a word for "you" (tu) here?

In Italian, you usually drop the subject pronouns like io (I) or tu (you) because the verb's ending already tells us who is doing the action. The -i at the end of abiti makes it clear that it means "you live". Saying Dove tu abiti ora? sounds a bit clunky unless you are trying to specifically emphasize the word "you".

I've also seen the word adesso used for "now". Could I use it here instead of ora?

Absolutely! Both ora and adesso mean "now", and they are completely interchangeable in Italian. You could easily say Dove abiti adesso? and it would mean exactly the same thing.