I don't believe that Ben told Juliet that he'd let her go if she helped him get his operation, I think he blackmailed her with a you do this or I'll do that...
Ben did need the operation to happen so certainly completing his operation was imperative, that said, I think he was willing to let Sawyer, Kate and Carl go because he can always get them back if he needs them and Carl being with the losties assures that at least Alex and Carl won't be together. As for what Carl may tell the losties, Ben still feels he has the upper hand and the losties are at his beckon call if need be regardless of what they may think they know
I think that shooting Pickett was not in the discussion. Juliet made a decision to kill him, I think she hates him and all that he represents with regard to her own sense of being a hostage... she will have to pay the consequences for this!
Why would Juliet lie to Jack about what Ben said... she may still need an ally and isn't destroying any bridges... her goal is to get of the island and to that end she will do whatever she feels is necessary. The answer she gave to Jack solicits sympathy... and she knows Jack is a caring man.
