Ok, I'm intrigued. I noticed this is your second post on the EU.
Who is the President of the EU?
There isn't one, there's several. President of the Commission, President of the Parliament and (if the Treaty of Lisbon is ratified in all 27 Member States) a President of the Council of Ministers. Then the central bank has a President too.
There's no one President who holds the power - the most powerful roles are probably Commission President because the Commission initiates legislation (ie they write the first draft like a civil service) and the forthcoming Council President role because Ministers from all the Member States meet together to take joint decisions depending on their area of responsibility (ie environment ministers talk together about the environment, transport ministers on transport etc.) and that Presidnet's role will be to resolve conflict and set timetables.
Not all of the Member States subscribe to all of the policies (the UK for example is not part of the Euro - the common currency).
While some of the institutions have Headquarters in Brussels there is no central government. The Commissioners meet there but they are not a government - there's very little that they can agree without also getting agreement from Ministers from the Member States and also from the democratically elected members of the European Parliament. The European Parliament meets both in Brussels and Strasbourg. And the Council of Ministers meets in Brussels and Luxembourg. The Heads of State and Government from all the Member states meet together 4 times a year, usually in Brussels to set the strategic direction.
The EU started as a free trade area but it because clear over time that a level playing field between the Member States required some wider agreements (as just one example lorry drivers tired from driving across the continent need breaks so that people at the end of their routes are not disproportionately affected by accidents caused by tired drivers). There are some areas (trade, environment) where these countries have decided you can achieve more by agreeing to work together, not because any one of theme could nuke or fight the others into non-existence. The Court that can overrule national law has been doing so since 1974 - if you are going to agree to rules they need to be enforceable, equally, everywhere.
At the end of the day, there are still some people who see the future of the EU being as you portray it. but that's not the majority in Europe, and it's not even the majority of those inside the EU institutions any more. The new former Commmunist member states in particular feel they've fought too long and too hard to be themselves to be subsumed into another superstate and as the direction of the EU needs their agreement as well as those of all the other Member States I think it's highly unlikely that that is the ultimate destination now. So what is the EU and what is it for? It's a unique journey in pooling sovereignty for mutual benefit on equal terms.
You are right America does not belong to the EU. I'd be interested to see an application. Geography need not be an impediment to this (see past applications from Marocco, current negotiations with Turkey etc.) but shared values are important e.g. abolition of the death penalty as barbaric, no Guantanemo bay equivalents etc.
I could write now but I expect you have some questions or issues you'd like to talk more about? I'm happy to help where I can.