Q1: Can I activate this card’s inherited effect even if my opponent's Digimon and the Digimon that has this card in its digivolution cards are deleted at the same timing?
No, you can't activate it.
Lv.4 Growlmon (X Antibody) EX8-012 C Champion | Virus | Dark Dragon/X Antibody [Digivolve] [Growlmon]: Cost 0 [When Digivolving] <Draw 1> and trash 1 card in your hand. Then, if [Growlmon] or [X Antibody] is in this Digimon's digivolution cards, until the end of your opponent's turn, this Digimon gains "[On Deletion] You may play 1 card with [Guilmon] in its name from your trash without paying the cost." --- Inherited: [Your Turn] [Once Per Turn] When any of your opponent's Digimon are deleted, gain 1 memory.
Lv.4 Growlmon (X Antibody) EX8-012 C Champion | Virus | Dark Dragon/X Antibody [Digivolve] [Growlmon]: Cost 0 [When Digivolving] <Draw 1> and trash 1 card in your hand. Then, if [Growlmon] or [X Antibody] is in this Digimon's digivolution cards, until the end of your opponent's turn, this Digimon gains "[On Deletion] You may play 1 card with [Guilmon] in its name from your trash without paying the cost." --- Inherited: [Your Turn] [Once Per Turn] When any of your opponent's Digimon are deleted, gain 1 memory.
Lv.4 Growlmon (X Antibody) EX8-012 C Champion | Virus | Dark Dragon/X Antibody [Digivolve] [Growlmon]: Cost 0 [When Digivolving] <Draw 1> and trash 1 card in your hand. Then, if [Growlmon] or [X Antibody] is in this Digimon's digivolution cards, until the end of your opponent's turn, this Digimon gains "[On Deletion] You may play 1 card with [Guilmon] in its name from your trash without paying the cost." --- Inherited: [Your Turn] [Once Per Turn] When any of your opponent's Digimon is deleted, gain 1 memory.
Lv.4 グラウモンX抗体 EX8-012 C 成熟期 | ウィルス種 | 魔竜型/X抗体 「グラウモン」:コスト0 【進化時】≪1ドロー≫し、自分の手札1枚を破棄する。その後、このデジモンの進化元に「グラウモン」/「X抗体」があるなら、相手のターン終了まで、このデジモンは「【消滅時】自分のトラッシュから、名称に「ギルモン」を含むカード1枚をコストを支払わずに登場できる。」の効果を得る。 --- Inherited: 【自分のターン】[ターンに1回]相手のデジモンが消滅したとき、メモリー+1。