This planet can conveniently support up to 10-12 billion people (I mean food, water, living space, etc) at the present technological level. It can be more.
Overpopulation IS a problem but there's still some room. Besides, there are oceans too. And they too can be colonized.
Energy is not a problem, after all even with nuclear power we can produce enough energy for all.

The only question is - rich countries can afford it and poor countries - don't. This all can be eliminated once the countries disappear. Of course, in some areas people will live better than others but gradually this will averages out. This won't eliminate 90/10 ratio, however, 90% of the world's resources will be controlled by 10% of people but that's another story or the next step if you want.
Globalization will destroy the institution of international politics and currencies and international trade but will not solve any sociologic problems. I don't think that 'unification' will come peacefully. There bound to be some local conflicts but I don't think that things would deteriorate (although the scenario of a global conflict cannot be ignored completely). As Europe has united so will the Middle East, Asia, South America. We'll have 10-15 'megastates' in the beginning. North America and Europe will probably join next (and probably Australia), then it will probably be Asia and Africa - look at Asia I think that everything will be rotating around China the next decade and its influence in the region will grow more and more. (I really don't know whom Russia will stick to and I really wonder about it). If there will be no global conflicts (and I hope there wouldn't be anything like that) the further integration will gradually continue. Free travel is the cornerstone of this process.