I refer you to Vault 21.
R.I.P.
What's so bad about that?
It was a building in his land he did not own and could easily aquire. So he bet the residents and won, filling the vault with concrete. They didn't have to gamble, all they lost was their home (most of it).
The NCR has a lot worse things in their history, such as irradiating Vault City's water supply so they would agree to be annexed, the Bitter Sprins Massacre, and the mercenaries sent to Jacobstown.
The NCR is a democratic federation and a democratic government can't exist without public support. So, yes they do "care" about their own people. They have to, if for no other reason that if they don't demonstrate concern for their own citizens, they wouldn't have any.
The real question seems to be whether or not they put their concern for their people over and above their mandate to further expand their territory. I would say no. They have a tendency to bite off more they can chew in the name of expansion, which in turn, puts their people, citizens and soldiers alike, at significant and some might say, unnecessary risk. The NCR is clearly unable to allocate the necessary resources and manpower required to firmly shore up the territory that they have. I'm not going to say "greedy", but I think "overzealous" is a fair description.
Not exactly.
They are a republic, their representatives are voted into office. However I believe that in F2 they stated that the President is appointed by Congress (not sure whether that's right or wrong).
So techincally (if representatives' terms are very long) it could be a long gap between the NCR's government caring for its people (which it currently seems like it does not).