In the first movie, when the CIA is going over Marie's background, the agent analyzing her profile mentions she has Gypsy heritage. With this in mind, this may be a factor in why she was getting such lousy treatment at the U.S. Embassy in Switzerland, as well as why she can't seem to hold down a steady job and is always on the move.
Her sympathy to fellow 'wanderers' might be one of the reason she gets along with Bourne.
Bourne's memory loss wasn't just because of the gunshot wounds he suffered, but from what happened immediately beforehand: he encountered Wombosi with his children right as he was about to assassinate him. Given that the whole point of the assassination was to make it look like a Bodyguard Betrayal, that meant he would have had to kill anyone who saw him do the deed, including them. When faced with the fact that he would have to kill three children for the first time, he probably began to experience a Heroic BSoD as the full enormity of his ruthless career catches up to him. The gunshots afterward were just the icing on the cake.
In Ultimatum, the fact that the CIA can literally sedate and kidnap a guy in broad daylight, in front of dozens of shocked witnesses, in a foreign country, and get it away with it with a terrorism excuse is pretty unnerving. Especially since the guy in question is totally innocent and just had the bad luck to be standing next to Ross.