

Q1: Does this card's inherited effect also trigger when one of my opponent's effects plays my Digimon?
Yes, it does.
Q2: When a Dobermon with BT10-011 Canoweissmon and Gammamon with an On Play effect in its digivolution cards digivolves into this card, does this card's When Digivolving effect activate the On Play effect on both this card and the Gammamon digivolution card?
Yes, they activate.
Lv.4 Dobermon (X Antibody) EX5-059 U Champion | Virus | Dark Animal/X Antibody [On Play] 1 of your Digimon gains <Retaliation> until the end of your opponent's turn. [When Digivolving] <Draw 1>. Then, trash 1 card in your hand. If [Dobermon] or [X Antibody] is in this Digimon's digivolution cards, activate this Digimon's [On Play] effects. --- [Your Turn] [Once Per Turn] When an effect plays one of your Digimon, gain 1 memory.
Lv.4 Dobermon (X Antibody) EX5-059 U Champion | Virus | Dark Animal/X Antibody [Digivolve] [Dobermon]: Cost 0 [On Play] 1 of your Digimon gains <Retaliation> until the end of your opponent's turn. [When Digivolving] <Draw 1>. Then, trash 1 card in your hand. If [Dobermon] or [X Antibody] is in this Digimon's digivolution cards, activate this Digimon's [On Play] effects. --- [Your Turn] [Once Per Turn] When an effect plays one of your Digimon, gain 1 memory.
Lv.4 Dobermon (X Antibody) EX5-059 U champion | Virus | Dark Animal/X Antibody [Digivolve] [Dobermon]: Cost 0 [On Play] 1 of your Digimon gains <Retaliation> until the end of your opponent's turn. [When Digivolving] <Draw 1> Then, trash 1 card in your hand. If [Dobermon] or [X Antibody] is in this Digimon's digivolution cards, activate this Digimon's [On Play] effects. --- [Your Turn] [Once Per Turn] When an effect plays one of your Digimon, gain 1 memory.
Lv.4 ドーベルモンX抗体 EX5-059 U 成熟期 | ウィルス種 | 魔獣型/X抗体 【登場時】相手のターン終了まで、自分のデジモン1体は≪道連れ≫を得る。 【進化時】≪1ドロー≫。その後、自分の手札を1枚破棄する。このデジモンの進化元に「ドーベルモン」/「X抗体」があるなら、このデジモンの【登場時】効果を発揮する。 --- 【自分のターン】[ターンに1回]効果で自分のデジモンが登場したとき、メモリー+1。