What you're saying has merit, but the show tried to explain these things.  Jamie thought she was videotaping their meeting, which would have been bad for him, like really bad.  Three high-level business / political people discussing how they just got caught committing a bunch of felonies that they were conspiring…

Ames isn't a professional killer.  He's some money man.  I'm guessing he's never been in such a situation, and is probably why he reacted so badly to Jamie's idea of killing her.

Ames isn't a professional killer.  He's some money man.  I'm guessing he's never been in such a situation, and is probably why he reacted so badly to Jamie's idea of killing her.

Didn't she ask Alexi to come to the pier after she was being chased?

"Obviously no threat to her."