Q1: What order do an effect that triggers when a card is removed from a security stack and a Security effect on a checked card activate when they trigger simultaneously upon a security check?
The Security effect will activate first. Upon a security check, a Security effect will immediately activate without pending activation.
Q2: A Digimon that has this card in its digivolution cards attacks, and a security check was performed on my opponent's security stack. If the attacking Digimon with this card in its digivolution cards digivolves into a Digimon with Security Attack +1 using this card's inherited effect, is another security check performed?
Yes, another security check is performed.
Q3: I use a Digimon that has this card in its digivolution cards to perform a security check on my opponent's security stack, then I use this Digimon's inherited effect to digivolve into [[BT21-024|BT21-024 Cyberdramon]]. What card is trashed by [[BT21-024|BT21-024 Cyberdramon]]'s When Digivolving effect at such times?
The top card of the security stack. Upon a security check, the checked card is already considered to be removed from the security stack, therefore that card won't be trashed.
Lv.2 Gigimon BT21-001 C In-Training | Lesser/LIBERATOR - --- Inherited: [Your Turn] [Once Per Turn] When your opponent's security stack is removed from, 1 of your Digimon may digivolve into a Digimon card with the [Reptile] or [Dragonkin] trait in the hand with the digivolution cost reduced by 1.
Lv.2 Gigimon BT21-001 C In-Training | Lesser/LIBERATOR - --- Inherited: [Your Turn] [Once Per Turn] When your opponent's security stack is removed from, 1 of your Digimon may digivolve into a Digimon card with the [Reptile] or [Dragonkin] trait in the hand with the digivolution cost reduced by 1.
Lv.2 Gigimon BT21-001 C In-Training | Lesser/LIBERATOR --- Inherited: [Your Turn] {{OncePerTurn}} When your opponent's security stack is removed from, 1 of your Digimon may digivolve into a Digimon card with the [Reptile] or [Dragonkin] trait in the hand with the digivolution cost reduced by 1.