I was wondering if a question is closed, then are views after the question is closed still counted towards total views? If the answer is yes then would that add to the total view count value towards earning the "Popular Question" family of badges?
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As far as I know, closing only affects the ability to add answers. The view count has nothing to do with that so it should be updated.
You can also still vote on them and they count for the badges.
Yes, the only discrimination done on views (basically) is not counting a lot of self-views.