Learn Dutch: Wil je ooit in de stad wonen? - Do you ever want to live in the city?

Yes, it belongs to the same group! While nooit means "never", ooit is its opposite and means "ever" or "someday" in the future. Don't confuse it with soms, which means "sometimes".

Why does the adverb ooit come right after je?

In a yes/no question, the verb and subject swap places, so the sentence starts with Wil je. Adverbs of time and frequency usually come immediately after the subject in these types of questions, which is why ooit sits exactly where it does.

Could I say "Wil je in de stad ooit wonen?" instead?

No, that would sound unnatural. Dutch sentences generally follow a "Time before Place" rule. Since ooit (ever) tells us about time and in de stad (in the city) tells us about place, ooit must come first.

Why is wonen placed at the very end of the sentence?

This happens because of the verb willen (to want). When you use a modal verb like willen, kunnen, or moeten, it takes the main spot at the beginning of the question, and the actual action verb (wonen) gets pushed all the way to the end in its full infinitive form.