If 2 Digimon including a Digimon that has an "effects don't affect" effect are chosen for a "may battle" effect, can those Digimon battle?
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Yes, they can battle. A card that has an "effects don't affect" effect can still be chosen for an effect. In addition, a battle itself is a rule that compares DP, not an effect. Therefore, a Digimon that isn't affected by effects can be chosen, and then it can battle. If it loses the battle, it will be deleted as normal according to the rules.
During an attack by this card, I used its [All Turns] effect to have it and an opponent's Digimon battle, and my opponent's Digimon was deleted in battle. Then, if the attack target successfully becomes an opponent's Digimon and it's also deleted in battle, do I use this card's <Piercing> to perform 2 security checks?
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No, you only perform 1 security check for <Piercing>. Only 1 security check can be performed during a single attack, even if <Piercing> activates multiple times. However, if the number of security checks is modified by <Security A.>, that number of cards will be checked in a single security check.
During an attack by this card, I used its [All Turns] effect to have it and an opponent's Digimon battle, and my opponent's Digimon was deleted in battle. Then, if the attack target successfully becomes an opponent's Digimon, it loses the battle, but an effect prevents it from being deleted, can I still activate this card's <Piercing>?
Show ruling
Yes, you can. <Piercing> is an effect that triggers and activates if an opponent's Digimon is deleted in battle during the attack, and it's processed immediately before the end of attack timing. <Piercing> will still trigger if the Digimon with <Piercing> successfully attacks a Digimon, even if another battle occurs during this battle.
