Is there like an exhibit or Museum dedicated to the closest Encounters of the Third Kind movie that was filmed there?

No. Because the movie was not filmed there it eas filmed on a set. The ranger station is rather informative though but again nothing to do with aliens, the ones from outer space of course, or abductions ot UFOs or string theory or none of that nonsense.

No, unfortunately.

Nope. But at night you can see the stars.

Not that I recall

I didn't see one.