Q1: Can this card be placed under a tamer in a "Material Save" of a Digimon with "Dorlmon" in the DigiXros conditions, such as "BT10-013 Shoutmon X5"?
No, it cannot. This card can also be treated as "Dorlumon" only in DigiXros.
Lv.5 JaegerDorulumon BT19-038 R Ultimate | Virus | Beastkin/Xros Heart [Digivolve] Lv.4 w/[Xros Heart] trait: Cost 3 This card is also treated as [Dorulumon] for DigiXros. [On Play] [When Digivolving] Suspend 1 of your opponent's Digimon. Then, until the end of their turn, 1 of their Digimon can't activate [When Digivolving] effects or unsuspend. [On Deletion] You may place 1 Digimon card with the [Xros Heart] or [Blue Flare] trait from your hand or trash under any of your Tamers. --- Inherited: [Your Turn] This Digimon with the [Xros Heart] trait gains <Piercing>.
Lv.5 JaegerDorulumon BT19-038 R Ultimate | Virus | Beastkin/Xros Heart [Digivolve] Lv.4 w/[Xros Heart] trait: Cost 3 This card is also treated as [Dorulumon] for a DigiXros. [On Play] [When Digivolving] Suspend 1 of your opponent's Digimon. Then, 1 of their Digimon can't activate [When Digivolving] effects or unsuspend until the end of their turn. [On Deletion] You may place 1 Digimon card with the [Xros Heart] or [Blue Flare] trait from your hand or trash under any of your Tamers. --- Inherited: [Your Turn] This Digimon with the [Xros Heart] trait gains <Piercing>.
Lv.5 イェーガードルルモン BT19-038 R 完全体 | ウィルス種 | 獣人型/クロスハート 特徴に「クロスハート」を持つLv.4:コスト3 このカードはデジクロスで「ドルルモン」としても扱う。 【登場時】【進化時】相手のデジモン1体をレストさせる。その後、相手のターン終了まで、相手のデジモン1体の【進化時】効果は発揮せず、アクティブにならない。 【消滅時】自分の手札/トラッシュから、特徴に「クロスハート」/「ブルーフレア」を持つデジモンカード1枚を自分のテイマーの下に置ける。 --- Inherited: 【自分のターン】特徴に「クロスハート」を持つこのデジモンは≪貫通≫を得る。