Yes, that's Mal's gun underneath - specifically the Model 47A edition that was limited to 47 pieces, all metal construction. You cannot see from the photos, but Jayne's pistol is also in there (the all-metal Richard Coyle version) and one of the communicator boxes they used in the show (real, not resin).
The Indiana Jones hat is one made by Steve Delk, the hatmaker for Indiana Jones IV, but he made it in the Raiders-style, which he perfected. The whip is an actual David Morgan, who made them for the first three movies.
The case is closed top to bottom with glass shelves and internal lighting. They are Henredons from the 1980s. I got them as a kind of gift/inheritance from my parents. It's weird - they bought these when I was playing with G.I. Joes on the floor in front of them and now those same G.I. Joes are in those very cases in my home!