Q1: Do cards trashed from my opponent’s security stack by this card's When Attacking effect activate their Security effects?
No, the cards weren't being flipped over by a security check, so their Security effects 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 their last 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.7 Gallantmon Crimson Mode EX2-073 SEC Mega | Virus | Holy Warrior [When Digivolving] Delete all of your opponent's Digimon with the highest DP.[When Attacking] Trash the top card of your opponent's security stack. Add 1 to the number of cards trashed by this effect for every 10 cards in your opponent's trash.
Lv.7 Gallantmon Crimson Mode EX2-073 SEC Mega | Virus | Holy Warrior [When Digivolving] Delete all of your opponent's Digimon with the highest DP.[When Attacking] Trash the top card of your opponent's security stack. Add 1 to the number of cards trashed by this effect for every 10 cards in your opponent's trash.
Lv.7 Gallantmon: Crimson Mode EX2-073 SEC mega | Virus | Holy Warrior [When Digivolving] Delete all of your opponent's Digimon with the highest DP. [When Attacking] Trash the top card of your opponent's security stack. Add 1 to the number of cards trashed by this effect for every 10 cards in your opponent's trash.
Lv.7 デュークモン:クリムゾンモード EX2-073 SEC 究極体 | ウィルス種 | 聖騎士型 【進化時】最もDPが高い相手のデジモン全てを消滅させる。【アタック時】相手のセキュリティを上から1枚破棄する。相手のトラッシュ10枚ごとに、この効果で破棄する枚数を+1する。