I honestly believe Australia has the best system in the world, i.e. the parties congresmen/women & senators vote for who they want to lead, then depending on how many electorates you win, you become President with the ruling party.
IRV is mediocre, though, and can lead to unrepresentative results. It also does, on its own, protect against gerrymandering (though Australia presumably has some sort of independent district-drawing committee; not sure how it works). And the Australian Senate is possibly even worse than the US Senate, though at least it doesn't have arcane cloture rules.
Indeed, had the Presidency been elected by the popular vote with a runoff, the Civil War would at the very least been delayed a while, for it would have been impossible for the Republicans to win the White House under such a scenario.
Debatable at best. Given the choice between Lincoln and Breckinridge, I suspect most Douglas voters would have gone with Lincoln. At the very least, not enough would have gone with Breckinridge for him to win, since Breckinridge + Bell was still well short of Lincoln. Of course, Breckinridge voters would have reluctantly supported Douglas, but the breakdown of the Democratic Party would have been more severe at that point, and you have no guarantee that a Douglas type would ever manage the nomination (probably not).
