A player is eligible for the Champions League if you declare him available before the tournament starts when you are required to submit a list. Also, around midseason, you can pick replacements (3 moves and removing a guy from the eligible list counts as a move.)
As far as Eagles not being good in your game, I would guess it is just the variability that seems to exist in every game of FM.
Looks like you have some nice pickups
I really do want to manage Chelsea one day
