Q1: I use this card's When Attacking effect to trash my opponent's Security Cards. Do the security effects on those cards activate?
No. They weren't flipped over in a security check, so they don't activate.
Q2: My opponent has 1 or more cards in their security stack. I attack my opponent with this Digimon and its When Attacking effect trashes the rest of their security cards, leaving them with zero cards in their security stack. If the attack isn't blocked and my attack is successful when they have zero cards in their security stack, do I win the game?
Yes, you do.
Lv.6 Gallantmon BT2-020 SR Mega | Virus | Holy Warrior/Royal Knight [When Digivolving] If you have a red Tamer in play, delete 1 of your opponent's Digimon with 6000 DP or less.[When Attacking] Trash 1 of your opponent's security cards for every 10 cards in their trash.
Lv.6 Gallantmon BT2-020 SR Mega | Virus | Holy Warrior/Royal Knight [When Digivolving] If you have a red Tamer in play, delete 1 of your opponent's Digimon with 6000 DP or less.[When Attacking] Trash 1 of your opponent's security cards for every 10 cards in their recycle bin.
Lv.6 Gallantmon BT2-020 SR Mega | Virus | Holy Warrior/Royal Knight [When Digivolving] If you have a {{Colour|red}} Tamer in play, delete 1 of your opponent's Digimon with 6000 DP or less. [When Attacking] Trash 1 of your opponent's security cards for every 10 cards in their trash.
Lv.6 デュークモン BT2-020 SR 究極体 | ウィルス種 | 聖騎士型/ロイヤルナイツ 【進化時】赤の自分のテイマーがいるとき、DP6000以下の相手のデジモン1体を消滅させる。 【アタック時】相手のトラッシュ10枚ごとに、相手のセキュリティを1枚破棄する。