

Q1: Do I delete the Digimon that was played by this card's Your Turn effect at the end of the turn?
Yes, it's deleted upon the deletion timing.
Q2: What is the processing order for an effect that triggers at the end of the turn and the deletion of a Digimon played by this card's Your Turn effect?
The pending processing for the effect that triggers at the end of the turn and the deletion at the end of the turn are considered to be processing that triggers simultaneously. Therefore, the turn player can choose the processing order.
Mirai Kinosaki EX11-061 R LIBERATOR [Start of Your Main Phase] If your opponent has a Digimon, gain 1 memory. [Your Turn] When any of your Digimon digivolve into a [Puppet] trait Digimon, by suspending this Tamer, you may play 1 level 3 [Puppet] trait Digimon card from your hand without paying the cost. At turn end, delete the Digimon this effect played. --- [Security] Play this card without paying the cost.
Mirai Kinosaki EX11-061 R LIBERATOR [Start of Your Main Phase] If your opponent has a Digimon, gain 1 memory. [Your Turn] When any of your Digimon digivolve into a [Puppet] trait Digimon, by suspending this Tamer, you may play 1 level 3 [Puppet] trait Digimon card from your hand without paying the cost. At turn end, delete the Digimon this effect played. --- [Security] Play this card without paying the cost.
Mirai Kinosaki EX11-061 R LIBERATOR [Start of Your Main Phase] If your opponent has a Digimon, gain 1 memory. [Your Turn] When any of your Digimon digivolve into a [Puppet] trait Digimon, by suspending this Tamer, you may play 1 level 3 [Puppet] trait Digimon card from your hand without paying the cost. At turn end, delete the Digimon this effect played. --- [Security] Play this card without paying the cost.
城之崎観来 EX11-061 R リベレイター 【自分のメインフェイズ開始時】相手のデジモンがいるなら、メモリー+1。 【自分のターン】自分のデジモンが特徴に「パペット型」を持つデジモンに進化したとき、このテイマーをレストさせることで、自分の手札から、特徴に「パペット型」を持つLv.3のデジモンカード1枚をコストを支払わずに登場できる。ターン終了時、この効果で登場したデジモンを消滅させる。 --- 【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。