Q1: Does this card's Your Turn effect activate when the hand increases from the digivolution bonus upon digivolution by an effect?
No, it doesn’t activate.
Q2: If both my hand and my opponent's hand increase when we both draw 1 card from our decks using an effect such as BT16-020 GaoGamon's When Digivolving effect, does my opponent add 2 cards from the top of their security stack to the hand using this card's Your Turn effect?
No, they don’t. Although cards are added to both players' hands, they are added at the same timing, therefore your opponent only adds 1 card from their security stack to the hand.
Q3: Can I use this card's On Deletion effect to play a Tamer card even if I don't return a card from the trash to the hand?
Yes, you can.
Lv.6 AncientGarurumon BT17-028 SR Mega | Data | Ancient Animal/Ten Warriors [On Play] [When Digivolving] Return 1 of your opponent's Digimon with the lowest level to the hand. [Your Turn] [Once Per Turn] When an effect adds cards to your or your opponent's hand, your opponent adds the top card of their security stack to the hand. [On Deletion] You may return 1 Tamer card and 1 [Hybrid] trait Digimon card from your trash to the hand. Then, you may play 1 Tamer card from your hand without paying the cost. DigiXros -3: [Lobomon]×[KendoGarurumon] When you would play this card, you may place specified cards from your hand/battle area under it. Each placed card reduces the play cost.
Lv.6 AncientGarurumon BT17-028 SR Mega | Data | Ancient Animal/Ten Warriors [On Play] [When Digivolving] Return 1 of your opponent's Digimon with the lowest level to the hand. [Your Turn] [Once Per Turn] When an effect adds cards to your or your opponent's hand, your opponent adds the top card of their security stack to the hand. [On Deletion] You may return 1 Tamer card and 1 [Hybrid] trait Digimon card from your trash to the hand. Then, you may play 1 Tamer card from your hand without paying the cost. DigiXros -3: [Lobomon]×[KendoGarurumon] When you would play this card, you may place specified cards from your hand/battle area under it. Each placed card reduces the play cost.
Lv.6 AncientGarurumon BT17-028 SR Mega | Data | Ancient Animal/Ten Warriors [On Play] [When Digivolving] Return 1 of your opponent's Digimon with the lowest level to the hand. [Your Turn] [Once Per Turn] When an effect adds cards to your or your opponent's hand, your opponent adds the top card of their security stack to the hand. [On Deletion] You may return 1 Tamer card and 1 [Hybrid] trait Digimon card from your trash to the hand. Then, you may play 1 Tamer card from your hand without paying the cost. DigiXros -3: [Lobomon]×[KendoGarurumon]
Lv.6 エンシェントガルルモン BT17-028 SR 究極体 | データ種 | 古代獣型/十闘士 【登場時】【進化時】最もLv.の低い相手のデジモン1体を手札に戻す。 【自分のターン】[ターンに1回]効果で自分/相手の手札が増えたとき、相手は相手のセキュリティを上から1枚手札に加える。 【消滅時】自分のトラッシュから、テイマーカードと特徴に「ハイブリッド体」を持つデジモンカード1枚ずつを手札に戻せる。その後、自分の手札から、テイマーカード1枚をコストを支払わずに登場できる。 「ヴォルフモン」×「ガルムモン」 登場するとき、手札/バトルエリアからこのカードの下に置ける。1枚ごとに登場コストをマイナスする