A Few Sentences Needing A Quick Ameri-pick

Sentence one - "Sean understood the gist of it, that whatever it was had caused their immune systems to attack the part of their X chromosomes that their mutation was on, and that it was wearing off." Do Americans use gist?

Sentence two - "... even if what Hank wanted to change wasn't anything like as much as what Sean wanted to change - who even noticed other peoples's feet anyway?"

Sentence three - "Alex had been flashing anyone he could for a laugh." Does flashing mean the same thing in the US as over here?

Another usage question - does US English use 'jab' for injections?