I know that the NRA is like some big scary bogeyman to lots of people that is totally evil and devoid of any humanity whatsoever, but if the phrasing you gave their claims is accurate, then I have to agree with 2 of the three claims.

First, armed security guards at school.
I know it makes it look scary and militaristic, but these people are [ideally] trained professionals set in the schools for the sake of "guarding" "security".
I went to Leuzinger high school which was pretty much, for lack of a better word, "totally ghetto" and they had lots of security guards (male and female).
They didn't feel like some dark, evil presence on campus though, and even the kids who got in trouble all the time seemed to get along with them.
Sure, that was high school, but maybe an armed presence at elementary schools would teach kids the right attitude to have toward police: if you're not doin' anything wrong, then they don't have to be scary.
Basically, I'm saying that security guards, even armed ones, can be beneficial to both the safety of the school and to the growing worldview of the students.

Second, guns don't just get up and discharge themselves into crowds.
They have to be picked up, loaded, aimed, and the trigger has to be pulled.
That old cliche about "guns don't kill people, people kill people" ia a true one, so having better background and phychological tests for people trying to get permits to own a gun seems much more effective.

The thing about video games, I don't really agree with.
I know lots of gamers who play violent games (I myself am a huge survival horror fan) that aren't violent people.
I haven't done a lot of study on the issue though...

I don't personally own a gun, but I know people who do that aren't criminals, who don't think that life is expendable, and who aren't the cold-blooded monsters that gun-owners are made out to be lately.

But anyway, here's a PBS article about how most criminals get their guns: [link]
Most of them are bought illegally.

Sorry, I didn't mean to ramble on so long