Q1: Only the top card of my opponent's security card is face up. If this card's On Play When Digivolving effect activates, what security card is flipped to face up?

The 2nd card from the top of their security stack is flipped to face up.

Q2: What happens to cards placed face up in the security stack by effects?

They become face-up security cards that remain revealed. Other than rules that specify face-up security cards, the rules apply in the same manner as standard security cards.

Q3: What happens upon a security check for a security card that is placed face-up?

The check is performed with the card left revealed. Other than rules for cards left revealed, the rules apply in the same manner as standard security checks.

Q4: Does a card's Security effect trigger upon a security check with that card placed face-up?

Yes, it triggers.

Q5: What happens if I shuffle a security stack that includes security cards placed face-up?

Any face-up cards are placed face down, then you shuffle the cards. After shuffling, all cards are left face-down.

Q6: In what order do a Security effect, "when ... performs a security check" effect, and "when a card is removed from ... security stack" effect activate when they trigger simultaneously upon a security check?

Security effects take precedence for activation. Upon a security check, a Security effect will immediately activate without pending activation. For other triggered effects, the turn player activates their effects first.

Q7: If I attack with this card, an opponent's face-up security card is checked for the security check, then this card's Your Turn effect activates and I place the top card of this Digimon at the bottom of the security stack, does the End of Attack effect on the Digimon under this card trigger?

Yes, it triggers.

Q8: An opponent's Digimon attacks a player by an effect at the end of their turn. What happens if this card's {Security} End of Opponent's Turn effect then plays this card, my security stack is reduced to 0 cards, and the attack against the player is successful?

You lose the game.

Q9: What happens if this card has just BT15-086 Marvin Jackson in its digivolution cards, it performs a security check on a face-up security card, and this card's Your Turn effect activates?

This card stacked on top is removed, causing this Digimon to become a Tamer, therefore the attacking Digimon is considered to be removed.

Q10: This card has EX11-041 Oblivimon in its digivolution cards, it gained Security Attack +1, and it attacks a player. At such times, if the Your Turn effect activates upon the 1st face-up security check and this card's top stacked card is placed as a security card, do I use EX11-041 Oblivimon to perform the 2nd check?

Yes, you use EX11-041 Oblivimon to perform the 2nd check. If the 2nd check is on a face-up security card, EX11-041 Oblivimon's Your Turn effect will also trigger.