Here's a more technical explanation by Warren Smith, a Princeton math PhD whose work was the centerpiece of the book "Gaming the Vote".
Finally, see real world data from a century of IRV in Australia.
Australia has single-representative voting districts with instant-runoff voting, and they seem to have something that looks to me being close to a two-party system in practice. I admit, I didn't browse though all possible countries, so perhaps you know a better example?
There are much better single-winner systems available: see approval voting, score voting, and Condorcet voting. But if you want a legislature with proportional representation, you really need a system with multi-representative districts.
Third parties would greatly benefit from range-voting. I used to favor Condorcet voting methods as an improvement over plurality, but now I favor range-voting. Mostly for how much more straightforward the vote outcomes are, and the simplicity of explaining it. The no-show paradox inherent in Condorcet systems also bothers me.
There is a good summary of the properties of different voting systems on wikipedia.
That is a myth. Instant Runoff Voting does not eliminate the lesser evil (spoiler) problem. See this explained by a math PhD.