Why? The Roman empire, socially speaking, was far bigger than the world is today, because the fastest transportation (and communication) was on horseback. I'd imagine that a world state would function much more smoothly than the Roman empire ever did, simply because someone from South America can dial someone in Mongolia and communicate as if they were in the same room. If it works for people, why can't it work for a bureaucracy?
No, I'm saying that while warfare is available as a form of political coercion, it is always going to happen. If two actor in a unipolar system can't resolve their differences diplomatically, war is always going to be the proper choice for them unless the costs of it are too high.
Dunno about WWI, but definitely yes for WWII.
You're not engaging the issue. Yes, there are periods of stagnation in the path to unipolarity, but that doesn't raise any objections to the need for it. In the case of WWI, trenches made the benefits of warfare exponentially harder to achieve, and raised the costs of it to destructive levels. The aftermath was something like a political ice age.
WWII, on the other hand, was a very healthy conflict. It destroyed the European empires, which had no inherent geopolitical power, and left the real power in the hands of the two states which could maintain it.
