Q1: Does this card's Your Turn effect trigger when this card is in the breeding area and would digivolve into a card with the Puppet trait?
No, it doesn't trigger. Only effects with the Breeding icon trigger and activate in the breeding area.
Lv.3 Shoemon EX7-024 R Rookie | Virus | Puppet/LIBERATOR [Your Turn] When this Digimon would digivolve into a Digimon card with the [Puppet] trait, reduce the digivolution cost by 1. --- Inherited: [Your Turn] All of your opponent's Security Digimon get -3000 DP.
Lv.3 Shoemon EX7-024 R Rookie | Virus | Puppet/LIBERATOR [Your Turn] When this Digimon would digivolve into a Digimon card with the [Puppet] trait, reduce the digivolution cost by 1. --- Inherited: [Your Turn] All of your opponent's Security Digimon get -3000 DP.
Lv.3 Shoemon EX7-024 R Rookie | Virus | Puppet/LIBERATOR [Your Turn] When this Digimon would digivolve into a Digimon card with the [Puppet] trait, reduce the digivolution cost by 1. --- Inherited: [Your Turn] All of your opponent's Security Digimon get -3000 DP.
Lv.3 シューモン EX7-024 R 成長期 | ウィルス種 | パペット型/リベレイター 【自分のターン】このデジモンが特徴に「パペット型」を持つデジモンカードに進化するとき、支払う進化コスト-1。 --- Inherited: 【自分のターン】相手のセキュリティデジモン全てをDP-3000。