Do Americans realise (or care) about how much most people hate them?
People of many nations have a love-hate relationship with the United States. On one hand, they love certain aspects of American culture (e.g. rock'n'roll, Disney, etc.); on the other hand, they either envy American properity and/or fear American power. I don't think the average American is aware of this love-hate situation and, what they don't know about, they don't care about. The British think that most Americans are stupid...
I don't think the British have a "lock" on intelligence. Traditionally, the educational systems in each country emphasize different things; while both countries "track" students so that they are more likely to stay in the socio-economic strata of their parents, the British do this more effectively. In defense of Americans, at least they do not subject themselves to an heredity monarch who does not even have to pass the "11+ Exam" to be kept in luxury by the State.

Europeans think that Americans are greedy and that they eat far too much.
I would reject any notion that Americans individually or collectively are greedy. Quite to the contrary, Americans, individually, are very generous and, as a nation, have shed blood and given foreign aid money in great quantities. I think that the World's expectations of America are very high. It is clear that the average American eats too much.

Many areas of the world see Americans as being politically agressive.
I think the World would do well to reflect on post World War II Europe and the domination sought by the Soviet Union vs. the restraint shown by the United States.

Most other bits of the world see America as being politically naive.
Is that agressively naive? The United States, blessed with oceans to the East and West, has not had to concentrate on foreign policy quite as hard as some other nations. Does the average American know the difference between Switzerland and Sweden? No.

The feeling 'globally' is that Americans only really care about America.
Dear 'Mr. Global,' People of all nations care most about their own nation... nothing new there!

What's really different about the United States is a) it's made up of people from all over the world and b) most of the American people - or their forebearers - were either chased out of or starved out of the countries that complain about Americans today.

I was not born in the USA. By the time I was 16, I had lived in 4 different countries; by the time I was 32, I had been around the world twice. The last time I was out of the United States was last Friday. These are my thoughts.

All the best (and I mean it),
Dan