I just realized Kor's question never got answered.
1. When Angel is negated by Woes, the following happen:
- Justin Martyr goes back to territory and Angel comes back to battle.
- The 2 cards drawn go back on top of deck.
- Word of Their Testimony is cascade-negated, but since it was searched out with a CBI ability, it goes back to your hand.
2. See bullet point 3 in my answer for question 1.
3. I don't see why not. I would rule that you can discard Polycarp to "instead" the cascade-negation of WotT, which would keep it in battle (to immediately be discarded by game rule, since only Angel would be in battle at that time).
The fact that it is discarded immediately does not actually affect WotT's activation; by "insteading" the negation, it was never actually negated. It was played on a legal target when it was played (Justin), and wasn't negated, so it sticks.
