1. Yes. But if you look it up on most sites it'll be football.
2. Sometimes. Doesn't really matter. Different teams. Euro's are all the National team players. The top players. The Olympics is a U23 tournament. With 3 over age players allowed (but not Beckham it seems for Great Britain). So it's a lot of younger players. Don't really know of anyone who would play in both. Club teams wouldn't allow it. Still good football and you can get a look at the next up and coming stars.
3. They did not. Lost out to Mexico and Honduras. Actually lost in the group stage to Canada and tied El Salvador. Didn't even make it to the knockout stages to get a chance to qualify. Very poor. Were supposed to have a pretty good team also. Very poor.
4. Yes they are. Expected to win. Playing very well now. Beat most of their competition recently, albut in friendlies. They have to play a pretty good team in France in the group stages. For the women this is a big tournament. All the National Team players are there. (not a U23 competition) They are on NBC today at 2:00 (ET) playing Canada in a friendly as a send-off game.