Is there a military discount and senior discount for the museum and the planetarium?

I am unsure of the discount amount but they do have both. There website should have the appropriate discount amounts.

The museum is part of the blue star musems. Active duty get up to 5 family members in free when you show your military ID. https://bluestarfam.org/family-life/blue-star-museums/

Yes. However, the amount discounted depends on whether you plan on touring the museum only, or if you plan on seeing the planetarium, etc. The discount is around 2-3 dollars. Note though that Reno county residents can tour the Hall of Space Museum for free