As far as I know, Judaism is a religion, not a race.
Jews are an ethnic group, a defined people, with their own unique religion, language, history, folklore and genetic and physiological attributes.

you can be jewish and christain
Problematic. While a Jew doesn't have to be religious in order to be considered a Jew (provided he answers all the other parameters), actually converting to another religion is a bit tricky, since much of the Jewish culture relies on the Jewish religion and philosophy. It's just too much of a contradiction.

As for why Jews are hated... well, we'll start off with a statistic. 56% of Nobel Award winners are Jews. The overall percentage of Jews in the world's population is around 0.001% (about 13 million Jews total). Second, try to look up in your memory some of your favourite comedians, film-makers, or famous scientists. My point is... Jews are very prominant, vocal and visible, but their strength isn't in numbers. When they actually had to protect themselves, they often failed (up until the erection of the Jewish State of Israel), and because they are a powerful, educated and resourceful minority, they are also very much hated.

Also, the hatred towards Jews is so very old, it seems to have run in the cultural mentallity of many a people, especially in Europe. Connotations and associations with the word 'Jew' are not very positive ones.

DOES ANY OF IT REALLY MATTER?!
I think it does to the Jews, mostly.

this is an example
Dude, I think you just picked the ugliest Paratrooper in the Israeli army.

It's like saying arabs are people who blow themselves up for anything, or that north americans are fat ass uncultures rednecks that only watch football on TV all day and love the flag, etc.
Too many Arabs blow themselves for it not to be considered a norm, and many Americans are indeed fat, ignorant and love the flag. There's a reason stigmas are born... Jews often mess around with money more than others do, and they have an obvious knack for it, just to specify about one of the many stereotypes.

However, I don't understand how their religion or race is related to that. Maybe it's not even related.
Of-course it's related. Judaism teaches that education is one of the foundations for a good, stable and moral society - and thus, those teachings have survived through the ages, and have made into a cultural norm, a mentallity. Jewish mothers give their children books, before those can even tie their own shoe-laces, if you want to go the extreme.

America is in trouble because the jews have their hands in the goverments pockets
Actually, that may be quite true. Because of the powerful Jewish lobby, the US aids and supports Israel more than it would've normally, and that makes a lor of other nations in the world quite upset.