tedhl,
1) I agree with everyone that it is risky to try and connect so many times in one day. Highly likely that 1 flight might be delayed due to weather. ORD is known for weather delays.
btw, you might want to check the actual booking class for US domestic 1st class on a 1w business class ticket! I think that they may book in a different class and only credit you a business class trip even though it was in first class. I think BA did that to me!
2) Definitely don't want to do AA Eagle since they have no 1 class.
3) ?
4) AMS or Paris looks good. Try and make sure they are all out of Terminal 4 so it is easier for you.
5) As long as you don't stop. I.e. as silver said, there has to be a 'x' in the trip to indicate just a change of planes and no stopping.