Most of the labs have moved away from being owned by the public to being owned by corporations (Los Alamos is now owned by a company called LANS -- Los Alamos National Security -- partially owned by the University of California); my friends who have contracted at Los Alamos have mentioned a few times over that non-essential services have been scaled back if not completely cancelled. I'm assuming this is also the case -- if it's not "Core" to the lab, or part of the lab's mission, they're stepping away from it to keep their costs down.
It has nothing to do with ownership. Gov labs all over, regardless of ownership, have cut back to core operations due to the political climate of sequestration.
The labs are known as FFRDCs (Federally Funded Research and Design Centers.) They've been ran by private contracts since their inception.
Not all of the labs are FFRDCs though (also the D stands for development, not design), some are just non-profit corporations.
Yes my mistake on the acronym. And you're correct there are other labs with different structures such as UARCs or Lincoln Labs. But the point is that the government has never "owned" the labs. They've only funded them and have let them been run by private entities.
This is not correct...the DOE labs are government-owned, contractor operated (GOCOs). Except the one in Pittsburgh, which is owned and operated by the government.
No idea, but they recently shut down their public software mirrors, too: