1. Nope. When AI takes over, it means you and your opponent has lost connection with each other. This "timeout" can occur for many reasons ranging from temporarily slow connection, lag spikes, or just Flash slowing down on either of your PC. The latter occurs very often when either player tabs away from the game tab, which is the number one reason so many players time out in PvP1.
Manually leaving the game means the other player autowins.
2. See above.
3. See above. No, since they don't leave the duel in question.