On Corey, I'm in the stage of recovering from a migraine where I'm interested in things but don't have the energy to really chase them down, so:

Dunno! The Adams family had a lot of children and a lot of descendants, so there could be some stray cousin, but they seem pretty good at tracking and he's not on the main lists. http://henryadamsofbraintree.com/president-john-adams-descendants.html, f'rex.

ETA: Oh, right, acestry.com; I'm not subscribed ATM, but his mom was Julia Etta Reid McKenney Corey, and those names (that is, McKenney or Corey) don't show up as Adams-connected names.

ETA2: Also, urgent care Bad. Except insofar as it exists to help people, I mean.