Rulings
Q1: After using this Digimon's effect to digivolve it into AncientGreymon, I digivolve (or de-digivolve) it into another Digimon. Do I still have to delete it at the end of the turn?
Digimon carry over effects after digivolving or de-digivolving, so you still have to delete this Digimon at the end of the turn.
Q2: After using this Digimon's effect to digivolve it into AncientGreymon, I use BT5-109 Mega Digimon Fusion! to digivolve it into a level 7 Digimon. At the end of the turn, which effect takes precedence: This card's "delete this Digimon at the end of the turn" effect, or Mega Digimon Fusion!'s "return the Digimon that digivolved with this effect to the bottom of its owner's deck" effect?
They both trigger at the same time, so you can choose which order to activate them in. The one you activate first takes precedence.
Q3: After using BT3-109 Back for Revenge! on this Digimon, I use this Digimon's effect to digivolve it into AncientGreymon. When this Digimon is deleted at the end of the turn, which Digimon does Back for Revenge!'s effect allow me to re-play to my battle area? This card, or AncientGreymon?
Digimon carry over effects after digivolving, so AncientGreymon is the Digimon re-played in your battle area.
Data Sources
Lv.4 Agunimon P-029 P Hybrid | Variable | Wizard [When Attacking] This Digimon can digivolve into an [AncientGreymon] in your hand for a memory cost of 2, ignoring its digivolution requirements. If it does, delete this Digimon at the end of the turn. --- Inherited: [Your Turn] When digivolving this Digimon into an [AncientGreymon] in your hand, reduce its digivolution cost by 2.
Lv.4 Agunimon P-029 P Hybrid | Variable | Wizard [When Attacking] This Digimon can digivolve into an [AncientGreymon] in your hand for a memory cost of 2, ignoring its digivolution requirements. If it does, delete this Digimon at the end of the turn. --- Inherited: [Your Turn] When digivolving this Digimon into an [AncientGreymon] in your hand, reduce its digivolution cost by 2.
Lv.4 Agunimon P-029 P Hybrid | Variable | Wizard [When Attacking] This Digimon can digivolve into an [AncientGreymon] in your hand for a memory cost of 2, ignoring its digivolution requirements. If it does, delete this Digimon at the end of the turn. --- Inherited: [Your Turn] When you would digivolve this Digimon into an [AncientGreymon] in your hand, reduce its digivolution cost by 2.
Lv.4 アグニモン P-029 P ハイブリッド体 | ヴァリアブル種 | 魔人型 【アタック時】このデジモンは手札の「エンシェントグレイモン」に進化条件を無視して進化コスト2で進化できる。そうしたとき、このターン終了時、このデジモンを消滅させる。 --- Inherited: 【自分のターン】このデジモンが手札の「エンシェントグレイモン」に進化するとき、支払う進化コストを-2する。