This came up at the last tourney in teams, and I would also like to know for certain how these scenarios work. In the case of Levi, we ruled that his ability to discard didn't happen until the blocking team decided who was going to block, since territories aren't shared but the LoB is. I'm not sure about this though, I could probably see it going either way...
Levi (RA)
Type: Hero Char. • Brigade: Blue • Ability: 10 / 10 • Class: Warrior • Special Ability: If a captured Genesis Hero is in opponent's territory, discard a male human Evil Character from that territory. Levi has access to all Sites. • Identifiers: OT Male Human, Patriarch (Syria), Son of Jacob • Verse: Genesis 34:25