This seems like a dumb question but I'd like confirmation on it, so Shadows actions, knelt LotR Jaime, and dead WLL Theon all go off at the beginning of Dominance… in what order do these things happen? Shadows first and then first player chooses Jaime or Theon effect to go after resolution of Shadows? Or do Jaime and Theon go first (first players disgression) and then Shadows actions? Or does first player actually get to choose the order for all three?

Shadows rules says that you bring cards out of Shadows before any other "beginning of phase" passives.

Standing Jaime and discarding cards for Theon do not conflict, so there is nothing for the First Player to determine and they are considered to happen at the same time (assuming I am remembering the right versions of the characters).