Wand of dowsing + Divine intervension situation

[Groo]

Player A is lvl 9 and combats a monster - after a long fight, he defeats it
Player B is a cleric. Plays Wand of dowsing at the end of the combat - and takes Divine intervention from discard pile. Divine intervention, naturally resolves immediately Player B is also lvl 9.

Q1: is playing Wand of dowsing even possible to play during opponent's battle (player B is not involved in this battle)
Q2: Who wins the game?

Note: i know it's strange that player B plays Wand of dowsing so late - but in this particular situation he (player B) forgot Divine intervention is in the discard pile.