1) Yes. You can also use it when you discard it from your territory. You cannot use it when discarding from hand or set aside area, though.
This is not 100% accurate. The question also asked about being discarded due to a SA or being defeated in battle, but that only counts if YOU are the one doing the discarding. If YOUR SA causes the discard of an Assyrian, or YOUR numbers discard an Assyrian, then you can use PoJ. If your own Assyrian is defeated by the numbers or an opponent's SA, you may not use PoJ.
2) Captured characters retain their identifiers, but can only be targeted as captured characters (according to the REG). So I don't think it counts as having a Tabernacle priest in play, but I'm not 100% certain.
Captured Characters retain their identifiers, names, and titles for the purposes of cards that "look" for them, but
cannot target them because of them.
For example, a card like Bravery of David that says "if David is in play" can 'look' for David, and that part of the SA is satisfied even if he is captured. However, a card like Absalom's Soldiers that says "Place David beneath owner's draw pile" cannot 'target' a David that is captured.
This comes up a lot, see these threads:
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