Q1: The situation is that this card with "BT19-029 Tapirmon" as its digivolution card is in the Battle Area. When this card leaves the Battle Area due to an opponent's effect, can I activate this card's Opponent's Turns effect and play "Recovery +1 Deck" and then trash the security by the digivolution effect of "BT19-029 Tapirmon"?
Yes, it is possible. The All Turns effect of this card and the digivolution inherited effect of "BT19-029 Tapirmon" are triggered simultaneously. Players can activate them in any order they wish.
Lv.6 Dynasmon BT19-041 R Mega | Data | Holy Warrior/Royal Knight [On Play] [When Digivolving] By trashing your top security card, 1 of your Digimon gains <Blocker> and gets +6000 DP until the end of your opponent's turn. [All Turns] [Once Per Turn] When this Digimon would leave the battle area, if you have 2 or fewer security cards, <Recovery +1 ≪Deck≫>.
Lv.6 Dynasmon BT19-041 R Mega | Data | Holy Warrior/Royal Knight [On Play] [When Digivolving] By trashing your top security card, 1 of your Digimon gains <Blocker> and gets +6000 DP until the end of your opponent's turn. [All Turns] [Once Per Turn] When this Digimon would leave the battle area, if you have 2 or fewer security cards, <Recovery +1 ≪Deck≫>.
Lv.6 Dynasmon BT19-041 R Mega | Data | Holy Warrior/Royal Knight [On Play] [When Digivolving] By trashing the top card of your security stack, 1 of your Digimon gains <Blocker> and gets +6000 DP until the end of your opponent's turn. [All Turns] [Once Per Turn] When this Digimon would leave the battle area, if you have 2 or fewer security cards, <Recovery +1 (Deck)>.
Lv.6 デュナスモン BT19-041 R 究極体 | データ種 | 聖騎士型/ロイヤルナイツ 【登場時】【進化時】自分のセキュリティを上から1枚破棄することで、相手のターン終了まで、自分のデジモン1体は≪ブロッカー≫を得て、DP+6000。 【お互いのターン】[ターンに1回]このデジモンがバトルエリアを離れるとき、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》≫。