Rulings
Q1: If my opponent doesn't trash a security card for this card's Your Turn effect, which player performs <Recovery +1 (Deck)>?
You perform <Recovery +1 (Deck)>.
Q2: I have 0 security cards. If I activate this card's Main effect, do I delete my opponent's Digimon until they have 0 Digimon?
Yes, you delete their Digimon until they have 0 left.
Q3: I tried to delete my opponent's EX6-059 Barbamon using this card's Main effect. In response, my opponent uses Scapegoat on EX6-059 Barbamon to delete their other Digimon and prevent EX6-059 Barbamon from being deleted. At such times, is this card's "if this effect deleted" condition met?
No, it isn't met. The "if this effect deleted" condition is only met when a Digimon is deleted by this card's effect. In this case, EX6-059 Barbamon wasn't deleted by this card's effect, therefore the "if this effect deleted" condition isn't met.
Data Sources
Seventh Divine Cruz BT19-094 R Seven Great Demon Lords [Trash] [Your Turn] When any of your Digimon digivolve into [Lucemon (X Antibody)], by returning this card to the bottom of the deck, your opponent may trash their top security card. If this effect didn't trash, <Recovery +1 ≪Deck≫>. [Main] Delete your opponent's Digimon until they have as many as you have security cards. If this effect deleted, <Recovery +1 ≪Deck≫>. --- Inherited: -
Seventh Divine Cruz BT19-094 R Seven Great Demon Lords [Trash] [Your Turn] When any of your Digimon digivolve into [Lucemon (X Antibody)], by returning this card to the bottom of the deck, your opponent may trash their top security card. If this effect didn't trash, <Recovery +1 ≪Deck≫>. [Main] Delete your opponent's Digimon until they have as many as you have security cards. If this effect deleted, <Recovery +1 ≪Deck≫>. --- Inherited: [Security] You may play 1 [Lucemon] from your trash without paying the cost.
Seventh Divine Cruz BT19-094 R Seven Great Demon Lords [Trash] [Your Turn] When any of your Digimon digivolve into [Lucemon (X Antibody)], by returning this card to the bottom of the deck, your opponent may trash their top security card. If this effect didn't trash, <Recovery +1 (Deck)>. [Main] Delete your opponent's Digimon until they have as many as the number of your security cards. If this effect deleted, <Recovery +1 (Deck)>.
セブンス• ディバイン• クルス BT19-094 R 七大魔王 [トラッシュ]【自分のターン】自分のデジモンが「ルーチェモンX抗体」に進化したとき、このカードをデッキの下に戻すことで、相手は自身のセキュリティを上から1枚破棄できる。この効果で破棄しなかったなら、≪リカバリー+1《デッキ》≫。 【メイン】自分のセキュリティ枚数と相手のデジモン体数が同じになるように、相手のデジモンを消滅させる。この効果で消滅したなら、≪リカバリー+1《デッキ》≫。 --- Inherited: 【セキュリティ】自分のトラッシュから、「ルーチェモン」1枚をコストを支払わずに登場できる。