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1)While in Quest phase and having committed Thalin(+1 DMG to to each enemy as it is revealed) I draw Black Forest Bats which force me to remove a committed character. Which action is played first? Thalin's or the Bats' rule?
Instances where simultaneous effects occur, I usually choose the order in which they resolve, unless of course there is specific errata to clarify
2)In Combat Phase, when I attack, how many enemies can I attack? Only one?
Need more specific use case, but you can generally attack any number of enemies engaged with you, as long as your hero/character is not exhausted and able to fight.
3)I have committed two Heroes in the Quest phase. In Travel phase I choose to travel to Old Forest Road(After you travel to Old Forest Road, the first player may choose and ready 1 character he controls). Can I ready an already exhausted Hero who is committed for the quest?
Yes. Assuming of course you are the 1st player.
4)A Forest Spider is not defeated in Combat phase. Is his effect (After Forest Spider engages a player, it gets +1 attack until the end of the round) active on the next round?
No. Only on first engagement until the end of the round.