Pharaoh's Dungeon - Love it. Recommend using the word "hold" instead of "put". Maybe you could even extend the "regardless of protection" clause to Capture abilities used by your Pharaoahs, perhaps if Pharaoh's Throne Room is in play too, etc.
Book of the Law - Prefer OT Teal card instead of just Teal card. I like the phrase "all locations", as it is much shorter than "in play, hand, deck, discard, or set-aside" and whatever other locations get invented in the future.
Media - This might handcuff the playtesters in the future for the set-aside battlewinners they can create for Persians. As of right now, it's great.
Samaria - Recommend protecting from Discard Abilities, not just Discard. Are there currently any ways to give your opponents site access without their "approval"? I checked Priestly Crown, Temple Veil, and Salem, and none of them would. If there is a way, this becomes very powerful for certain defenses.
Herodian - Are "choose ability" abilities going to be defined so that they only identify which player gets to choose the abilities to be carried out? And that the controller of the ability, by definition, will choose how to carry them out? There are abilities, such as King Abijah, where the opponent must choose which bad option they want carried out, but they get to choose the targets.
Herodias - I would add, at the end of the first sentence, "...to search deck or discard for Beheaded or Rash Oath."
Storehouse - Not sure how I feel about it being able to TC recur EEs at the cost of 2 GEs. That's probably breakable somehow. Also, since the Storehouses were built to store up food during times of plenty, you could maybe build a trigger into this similar to Gifts of the Magi. Something like "When an opponent uses a Draw ability, you may place an OT enhancement from deck here, or you may exchange an OT enhancement here with an OT enhancement in discard."
As always, a solid swath of potential cards here