Q1: I used BT14-093 Emissary of Hope to digivolve this Digimon into a card with the Shaman or Wizard trait in my security stack. In such cases, can I use this card's Your Turn effect to trash cards from my security stack?
No, you can't. The period starting from the use of BT14-093 Emissary of Hope until the digivolution is complete and you shuffle your security stack is considered checking your security stack, so it isn't affected by other cards' effects. Therefore, you can't use this card's effect to trash cards from your security stack.
Lv.5 Boutmon P-074 P Ultimate | Beastkin | Vaccine [Your Turn] When this Digimon would digivolve into a card with [Shaman] or [Wizard] in its traits, you may trash up to 3 of your security cards. For each security card trashed with this effect, reduce the digivolution cost by 1. --- Inherited: [When Attacking] [Once Per Turn] If you have exactly 3 security cards, unsuspend this Digimon.
Lv.5 Boutmon P-074 P Ultimate | Beastkin | Vaccine [Your Turn] When this Digimon would digivolve into a card with [Shaman] or [Wizard] in its traits, you may trash up to 3 cards from the top of your security stack. For each security card trashed by this effect, reduce the digivolution cost by 1. --- Inherited: [When Attacking] [Once Per Turn] If you have 3 security cards, unsuspend this Digimon.
Lv.5 Boutmon P-074 P Ultimate | Vaccine | Beastkin [Your Turn] When this Digimon would digivolve into a card with the [Shaman] or [Wizard] trait, you may trash up to 3 cards from the top of your security stack. For each security card trashed by this effect, reduce the digivolution cost by 1. --- Inherited: [When Attacking] [Once Per Turn] If you have 3 security cards, unsuspend this Digimon.
Lv.5 バウトモン P-074 P 完全体 | ワクチン種 | 獣人型 【自分のターン】このデジモンが特徴に「神人型」か「魔人型」を持つカードに進化するとき、自分のセキュリティを3枚まで破棄できる。この効果で破棄したセキュリティ1枚ごとに、支払う進化コスト-1。 --- Inherited: 【アタック時】[ターンに1回]自分のセキュリティが3枚のとき、このデジモンをアクティブにする。