Q1: Can the inherited effect of this card be activated even if the opponent's Digimon and the Digimon that has this card as its digivolved card are deleted at the same time?
No, it cannot be activated.
Lv.4 Bulkmon BT20-032 C Champion | Vaccine | Dragonkin/Abadin Electronics/SEEKERS [Digivolve] [Pulsemon] or Lv.3 w/[SEEKERS] trait: Cost 2 [On Play] [When Digivolving] If you have 3 or more security cards, you may add your top security card to the hand. Then, if you have 2 or fewer security cards, <Recovery +1 ≪Deck≫>. --- Inherited: [All Turns] [Once Per Turn] When this Digimon deletes your opponent's Digimon in battle, gain 1 memory.
Lv.4 Bulkmon BT20-032 C Champion | Vaccine | Beastkin/Abadin Electronics/SEEKERS {{DigivolveFromNameOrTrait|2|Pulsemon|3|SEEKERS}} [On Play] [When Digivolving] If you have 3 or more security cards, you may add your top security card to the hand. Then, if you have 2 or fewer security cards, <Recovery +1 (Deck)>. --- Inherited: [All Turns] [Once Per Turn] When this Digimon deletes your opponent's Digimon in battle, gain 1 memory.
Lv.4 バルクモン BT20-032 C 成熟期 | ワクチン種 | 竜人型/AE社/シーカーズ 「パルスモン」か特徴に「シーカーズ」を持つLv.3:コスト2 【登場時】【進化時】自分のセキュリティが3枚以上なら、自分のセキュリティを上から1枚手札に加えられる。その後、自分のセキュリティが2枚以下なら、≪リカバリー+1《デッキ》≫。 --- Inherited: 【お互いのターン】[ターンに1回]このデジモンがバトルで相手のデジモンを消滅させたとき、メモリー+1。