Yes. These are the additional rulings from gatherer.wizards.com
10/4/2004 The power of the creatures when the effect resolves is used to determine how much damage is done.
10/4/2004 In multiplayer games, you can choose a different opposing player each time it the ability is activated.
10/4/2004 Either or both creatures can be tapped prior to using the ability and it still works.
9/25/2006 If either target is illegal at the time the ability resolves (whether because it has left the battlefield, because it has gained Shroud or Protection, or for any other reason), the ability taps the remaining target, but no damage is dealt. If both targets are illegal, the ability is countered.
Nope. You can only use one alternate cost when casting a spell. Flashback is an alternate cost, and so is casting it for 0 if an opponent has searched. You can only cast the Trap in this case for its flashback cost, not its alternate cost.
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You forgot to add 'as an additional cost discard two cards'
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But alas, we have to settle for an Alley.
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10/4/2004 The power of the creatures when the effect resolves is used to determine how much damage is done.
10/4/2004 In multiplayer games, you can choose a different opposing player each time it the ability is activated.
10/4/2004 Either or both creatures can be tapped prior to using the ability and it still works.
9/25/2006 If either target is illegal at the time the ability resolves (whether because it has left the battlefield, because it has gained Shroud or Protection, or for any other reason), the ability taps the remaining target, but no damage is dealt. If both targets are illegal, the ability is countered.