Q1: Can this card's End of All Turns effect End of Opponent's Turns choose not to trash opponent's security and can it delete one Digimon and one Tamer each from opponent?
No, we cannot. If security can be trashed, it must be trashed.
Lv.7 Lucemon: Satan Mode BT18-101 SEC Mega | Virus | Demon God [Digivolve] [Lucemon: Chaos Mode]: Cost 6 [When Digivolving] By playing 1 [Lucemon: Larva] from your trash to your empty breeding area without paying the cost, delete 1 of your opponent's Digimon or Tamers. [End of All Turns] [Once Per Turn] Trash your opponent's top security card. If this effect didn't trash, delete 1 of your opponent's Digimon and 1 of their Tamers.
Lv.7 Lucemon: Satan Mode BT18-101 SEC Mega | Virus | Demon God [Digivolve] [Lucemon: Chaos Mode]: Cost 6 [When Digivolving] By playing 1 [Lucemon: Larva] from your trash to your empty breeding area without paying the cost, delete 1 of your opponent's Digimon or Tamers. [End of All Turns] [Once Per Turn] Trash your opponent's top security card. If this effect didn't trash, delete 1 of your opponent's Digimon and 1 of their Tamers.
Lv.7 Lucemon: Satan Mode BT18-101 SEC Mega | Virus | Demon God [Digivolve] [Lucemon: Chaos Mode]: Cost 6 [When Digivolving] By playing 1 [Lucemon: Larva] from your trash to your empty breeding area without paying the cost, delete 1 of your opponent's Digimon or Tamers. [End of All Turns] [Once Per Turn] Trash your opponent's top security card. If this effect didn't trash, delete 1 of your opponent's Digimon and 1 of their Tamers.
Lv.7 ルーチェモン:サタンモード BT18-101 SEC 究極体 | ウィルス種 | 魔神型 「ルーチェモン:フォールダウンモード」:コスト6 【進化時】自分のトラッシュから、「ルーチェモン:ラルバ」1枚を空いている自分の育成エリアにコストを支払わずに登場させることで、相手のデジモン/テイマー1体を消滅させる。 【お互いのターン終了時】[ターンに1回]相手のセキュリティを上から1枚破棄する。この効果で破棄しなかったなら、相手のデジモンとテイマー1体ずつを消滅させる。