Q1: If I use this card's On Play When Digivolving effect to use an Option card from under a Tamer, what happens to that Option card?

As with the standard rules, a used Option card is temporarily treated as not being in any area. After using it and activating the Option card's Main effect, the card is trashed unless it's to be placed in an area.

Q2: If the "when you use an Option card" effect triggers, what is the timing when it can activate?

It can be activated after activating the used Option card's Main effect.

Q3: Does the "when you use an Option card" effect trigger if an Option card's effect activates by a method other than using the card?

No, it doesn't trigger. If an Option card's effect activates without using it, such as activation by a Security effect or Delay, the "when you use an Option card" effect doesn't trigger.

Q4: 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.

Q5: I tried to use this card's All Turns effect to place an opponent's Digimon as the bottom security card, but another effect prevented that Digimon from leaving. At such times, does this effect trash an opponent's security card?

No, it isn't trashed.

Q6: I tried to use this card's All Turns effect to place an opponent's Digimon as the bottom security card, but another effect prevented that Digimon from leaving. At such times, does it count as a use of this effect's Once Per Turn?

Yes, it counts. A use of X Per Turn occurs as soon as you choose to activate the effect. In this case, a use of Once Per Turn occurs as soon as you choose to place an opponent's Digimon as the bottom security card.