Q1: Can I use this card's End of Opponent's Turn effect to digivolve into a Digimon card with {{EffectLinkArchetype|Dex|DeathX}} in the trash regardless of its digivolution requirements?
No, this card's End of Opponent's Turn effect does not allow ignoring digivolution requirements, so you can only digivolve into a card that meets the digivolution requirements.
Tomonori Ryusenji BT17-090 R Abadin Electronics [Your Turn] When an effect places a Tamer card in one of your Digimon's digivolution cards, by suspending this Tamer, gain 1 memory. [End of Opponent's Turn] [Once Per Turn] If this Tamer is suspended, 1 of your Digimon with a Tamer card in its digivolution cards may digivolve into a Digimon card with [Dex] or [DeathX] in its name in the trash without paying the cost. --- [Security] Play this card without paying the cost.
Tomonori Ryusenji BT17-090 R Abadin Electronics [Your Turn] When an effect places a Tamer card in one of your Digimon's digivolution cards, by suspending this Tamer, gain 1 memory. [End of Opponent's Turn] [Once Per Turn] If this Tamer is suspended, 1 of your Digimon with a Tamer card in its digivolution cards may digivolve into a Digimon card with [Dex] or [DeathX] in its name in the trash without paying the cost. --- [Security] Play this card without paying the cost.
Tomonori Ryusenji BT17-090 R Abadin Electronics [Your Turn] When an effect places a Tamer card in one of your Digimon's digivolution cards, by suspending this Tamer, gain 1 memory. [End of Opponent's Turn] [Once Per Turn] If this Tamer is suspended, 1 of your Digimon with a Tamer card in its digivolution cards may digivolve into a Digimon card with [Dex] or [DeathX] in its name in the trash without paying the cost. --- [Security] Play this card without paying the cost.
龍泉寺智則 BT17-090 R AE社 【自分のターン】効果で自分のデジモンの進化元にテイマーカードが置かれたとき、このテイマーをレストさせることで、メモリー+1。 【相手のターン終了時】[ターンに1回]このテイマーがレスト状態なら、進化元にテイマーカードがある自分のデジモン1体をトラッシュの名称に「デクス」を含むデジモンカードにコストを支払わずに進化できる。 --- 【セキュリティ】このカードをコストを支払わずに登場させる。