Soyeong: The problem with trying to get rid of guns is that it would only be the law-abiding citizens who would turn them in, thus allowing criminals to act much more freely without having to worry about people defending themselves with guns. Not too long ago, there was a shooting at a movie theater. There were several movie theaters that played the same movies and were closer to where the shooter lived, but the one he picked was the only one in the area that had signs banning guns from the premises.
The issue had occurred to me, partly because that, I think, used almost word for word the same phrasing as Terry Pratchett over a similar idea in...Night Watch, I believe. Obviously that's a major issue, and I'm not sure how that would be addressed, I admit. On the other hand, I was more trying to point out that the guns probably hold a good deal more blame than the computer games. If you put the ability into peoples' hands to do something illegal, then the temptation will be there. If you put it into the whole population's hands, then you're almost sure to have some people giving in to that temptation. I don't know how topical this is in the US, but we don't blame Starbucks not paying tax in Britain on them having played a game involving setting up their accounts in another country (though I'm sure there are some around), but on a combination of them being generally a fairly unpleasant company and the tax system not being very good!
And even if it were possible to destroy all guns, that would simply mean that they would use other tools. Should we then ban all knives too? What about baseball bats?
Criminals tend to look for easy targets. If they see a target that they think could defend themselves, then they just look for an easier target. If it were highly probable that any given target was carrying a concealed weapon and was trained how to use it, then that would make mugging much riskier and much less likely to happen. In the case of the school shooting, it most likely would have been stopped quicker if the teachers had had guns.
The problem, which everyone arguing for giving more guns to people to give them an edge over criminals, is that without identifying said criminals (in which case presumably you'd deal with them before they kill people anyway) or making general distinctions based on race, location, etc most likely to kill people (and be, rightly, accused of racism, etc, so let's not go there) there's no way to avoid the criminals gaining the same increase! And while you can change the proportion of power resting in different portions of the population (as in your suggestion of the teachers having guns), this won't increase overall power, and increases the risk when, in this case, a teacher themself decides to start shooting people.
As for your first question, I can answer with reasonable certainty that guns are more dangerous than knives (although admittedly it may depend a bit on the gun), partly because they can do their damage faster. I've never been threatened by either weapon, but it strikes me that you have a few moments more to react to someone with a knife, as they have to get much closer to you, and even then you may have a better chance of dodging. Obviously knives shouldn't be banned, as they have other uses. Guns really don't have any use other than killing people, so I don't see that America with no guns (other than the army, for which they do have another utility: defending the country) would be any worse off than one with guns. That isn't really possible, as you point out, but blaming games for an issue which seems to me to sit squarely on letting people use firearms seems...ludicrous to me.