The American Civil War was a tragedy. Over half a million people died (the most in ANY military engagement in which the USA has been involved since), and the South's economy was destroyed (as it was essentially reliant on slavery). Of course, on the plus side, slavery was abolished (though it still took 100 odd years for it to be fully dismantled in reality).
But I don't think a civil war in Iraq would solve much at all. Both the USA and the CSA believed in the "United States", just with a bit of difference. Iraq, on the other hand, was formed from three different (and unrelated) former provinces of the Ottoman Empire by Britain, with no real aim or purpose other than to make sure that they and France were the only powers in the region. I doubt national identity and patriotism is as powerful in Iraq as it was in the USA during the 1860s. The country has undergone at least three separate coups since its independence in 1930, so it has not exactly been a stable nation.
As for the democracy issue, I think some sort of internet based "voting on issues" could work (and ditching parties and electoral colleges and dividing votes up between areas and such), though there are of course obvious issues; how do you decide what issues are going to get voted on? And you'd still need some sort of judicial system to prevent tyranny of the majority, an institution by its very nature undemocratic...
