SpaceX launched an NRO satellite last week.
Yep, and NRO launches are usually the domain of the United Launch Alliance (Lockheed/Boeing). SpaceX had to sue the US Government to compete for NRO launches..
Hhmm. I thought its previous test was its only test. Interesting.
There has been three X-37B missions - all three for the US Air Force. There's in fact an A variant that belongs to NASA that was used for drop tests (Like the Space Shuttle Enterprise did that for the Shuttle program). There's potentially a scaled up C variant that may be used to launch astronauts, but with the Boeing Starliner program I doubt this will happen.
The USAF has a whole separate space program since the 80's at least. It's like another NASA in terms of capability.
The two domains of focus are space and cyberspace. It is actually a joint venture with the NRO, NSA and USAF.
The USAF have had a space program separate to NASA since the early 60s (they wanted moon bases, space stations, the lot). In fact, it was the USAF and NASA that joined up to work on the Space Shuttle project as a consolidation between roles - with the USAF providing a lot of the post Apollo astronauts to NASA. A good example of this would be ex USAF Astronaut Bob Crippin, who flew on the first Shuttle mission with John Young.
I'm super surprised that I haven't heard anything about nations shooting each other's satellites down. Is that a thing that is done? If not, why not? And if so, why isn't it in the news?
Because we're not at war. And that would be an act of war.
What are they wearing that gear to protect against? Fuel explosion? Black oil? The Andromeda Strain?
Mostly down to hazardous substances used on the vehicle, such as hydrazine.