I came to this party late, so still at 0. Anyway...
Regarding OP, I read that as, "Let people have guns, and murder, robbery, and other violent crime rates will go down." I don't think he was looking at deaths by shooting (suicides, accidental, and crime-related), or even deaths in general, but overall crime statistics, which 'total gun deaths' doesn't really address.
Part of what makes this hard to analyze is that there are two distinct portions of each graph: the 'low gun control' (strictness ~40), and they have radically different behavior: low gun control states have essentially no correlation between strictness and any violent crime metrics, while for higher gun control states, the correlation is positive for murder and robbery, negative for rape, and null for 'property crimes' (slightly positive for 'overall' violent crime).
Another interesting thing, though, is that in pretty much all (except rape) statistics, both the highest and lowest crime rates are found in the 'low gun control' states; this suggests to me that crime rates have less to do with the availability of guns than with other factors particular to each state.
Regarding your last point, Washington DC is currently an experiment-in-progress.
The problem with your data is that it counts 'gun deaths', not crime levels. Your data includes suicides and accidental shootings with the violent crime. That's a very convenient set of data to present if your agenda is to outlaw gun ownership, but it's a bit disingenuous.
So I'm going to counter with a few graphs of my own.
First, http://img339.imageshack.us/i/89312727.png/
This is the one you already made: gun laws on the x axis, gun deaths on the y. I guess most people can be convinced there's a negative correlation there. Let's move on.
I assert that suicides contribute a significant amount to that correlation. In support, I present http://img691.imageshack.us/i/96131586.png/ (source: http://www.afsp.org/index.cfm?fuseaction=home.viewpage&page_id=05114FBE-E445-7831-F0C1494E2FADB8EA) as support. The shape of the two graphs is pretty similar. This kind of makes sense, because guns are a pretty effective way to kill yourself, but I digress. Instead...
http://img249.imageshack.us/i/21700353.png/
That's gun laws versus murder rates (source: http://www.infoplease.com/us/statistics/crime-rate-state.html). Suddenly the correlation is much less obvious. On the low end of strictness, data is all over the place, and on the high end, as availability of guns goes down, murders actually go up.
The same trend repeats with violent crime ( http://img220.imageshack.us/i/72421515.png/), property crime ( http://img260.imageshack.us/i/21861589.png/), and robbery ( http://img176.imageshack.us/i/84688439.png/). Interestingly, though, not with rape ( http://img519.imageshack.us/i/45149589.png/); can't really explain that one.
So, yeah. I don't think anyone would argue that more guns leads to more gun-related deaths (which the data you provided does show, however weakly), but we were never arguing about gun deaths. We were arguing about crime, where the correlations are much less clear-cut.
You asked for it...
A summary of some literature:
http://www.brown.edu/Administration/Provost/Advance/Valian%20Power%20Leadership%20&%20Politics.pdf
For peer-review...
http://www.advancingwomen.org/files/7/127.pdf
"Peer reviewers cannot judge scientific merit independent of gender."
For letters of recommendation...
http://das.sagepub.com/cgi/content/short/14/2/191
"Letters written for female applicants were found to differ systematically from those written for male applicants..."
There's a lot out there.
The legal system is part of the government. Losing this sort of lawsuit then is by definition the government stifling dissent. Or, to put it another way, without the government in place, the person bringing the lawsuit would be shit out of luck trying to punish someone for their speech.
Either way, you're wrong.
Happiness is twin floppies.