What is next week Wednesday?

The term “next Wednesday” always means two Wednesdays out. So on: Monday the 1st “this Wednesday” means Wednesday the 3rd. Monday the 1st “next Wednesday” means Wednesday the 10th.

Does next Wednesday mean this week or next week?

This is complex and depends on context. If it’s Tuesday then “next Wednesday” means 8 days from now. If it’s Sunday then it could be either the next Wednesday or the one after that, depending on the hand gestures used. But we’d probably use “this Wednesday” or “a week on Wednesday” to be clear.