If it's a power she possess, I do think it should be nullified by Jeffery at least the luck bit. Being able to analyze on the level that's available with his powers is really good for at least figuring out what's going on, but I honestly don't know how meta stuff meshes with Presence.
Unsure, Jeffery doesn't actually fight with Herah often in the series and when he does he'll leave her mostly to handle things on her own. He is specified however to act when he thinks he's going to have fun or when he thinks Herah can't win on her own. Most of Medaka's copied abilites (which seem to be her best way to incapacitate Herah) would call for Jeffery to use his powers on her. Plus, Herah would be acting kind out of character due to Medaka's plot manipulation which gives him more than enough reason to analyze either Herah or Medaka to help figure out what's going on.