From Britain, Happy Independence Day. If we hadn't lost the 13 colonies, we wouldn't have gone onto greater things (thinking India <3). It was the loss of the main of America that allowed Britain to become the greatest empire ever.
Not really, and you only become proper empire once you admit it. Right now all you got is pussy neo-colonialist BS. The fact is, although the US is powerful, comparatively it is nowhere near as powerful as Britain was. And even if it comes close, it never actually uses that power - possibly due to numerous failed interventions. In 1868, Britain just marched into Ethiophia as the emperor there was holding two Brits hostage. We burned too cities, killed 700 people, and secured it as part of the informal empire. How does the US treat its hostages in, say, North Korea? When the Chinese had the audacity to slightly restrict trade with European nations, British gunships steamed down the Yangtze river, blowing up cities as they went. The Chinese changed their mind. How does the US cope with the Chinese? As Lord Palmerston said, as in the days of old a Roman could claim "cives Romanus sum" and be confident of the protection of Empire, "a British subject, in whatever land he may be, shall feel confident that the watchful eye and the strong arm of England, will protect him against injustice and wrong." Those days are gone. But no Empire in the past or since has had such power over every country on the planet.
No indeed they didn't. But no one did. If you wanted a Nuclear war, there's this idea of a maximum number of effective nukes necessary. The US and Russia both have more than necessary - but that exactly outlines the situation. In nuclear terms, the US is rivalled (if not, by some metrics, outmatched) by Russia. Hell, Israel, France, Britain all have nukes too. This means the US is not the hegemon nuclear-wise. The British Empire was the hegemon, in almost every aspect, in its prime. We aren't comparing 'who is better, the US or British Empires', we're seeing how they stack up against the opposition of the time.
The extent of which the US and Russia have nukes means that it does not matter which one is superior. Each of them have more than double the nukes that all the other nations combined have, and can destroy each other many times over, along with the rest of the world.
To your first point: My idea exactly. There is no hegemon, as there is a balance. And yes, in a conventional sense it is, but that is missing the point.