What country did you visit during your last vacation. Which country is more formal. It doesn't make sense to use both 'have visited' and 'during your last vacation'. Have visited is in the present (like as of right now, you either have or have not done something before), but 'during your last vacation' is in the past.

Your choice of which and what is ok, but your tense choice doesn't feel natural to me. This would be a more natural way of asking the questions. Which countries did you visit during your last vacation? (Use past simple + during here) What countries have you visited? (Use present perfect to ask a question about an experience that happened in the past with no specific time related to it)