Wouldn't be caught dead = "Even If I were dead, I would be embarrassed by the situation, so I would never do it"
Wasn't playing with a full deck= "unprepared/incomplete," or possibly "stupid/mentally ill" (deck refers to a "deck of playing cards")
tightening the thumbscrews... I am a native speaker, and this one is new to me!
sang like a bird= "told everything" in the sense of telling details of a crime to the police or an authority figure, usually used disparagingly about someone who divulges information
pulled the wool over their eyes= "to trick/deceive"
missed the boat= "lost an opportunity"
see the back of that guy... haha, I don't know this one. Maybe means something like, "nice ass"
speak of the devil= example situation: we were just talking about john, and then john calls me on the phone. "speak of the devil, there's john now."
jump on the bandwagon: "join in whatever trend/idea is popular." Can be used disparagingly, though not necessarily