Q1: Can I put this card under a tamer in a "Material Save" of a Digimon with "Starmons" in the DigiXros conditions, such as "BT10-013 Shoutmon X5"?
No, it cannot. This card can also be treated as "Starmons" only in DigiXros.
Q2: Does this card's All Turns effect trigger when this card itself plays?
Yes, triggered.
Lv.4 ShootingStarmon BT19-035 R Champion | Data | Super Major/Xros Heart [Digivolve] Lv.3 w/[Xros Heart] trait: Cost 2 This card is also treated as [Starmons] for DigiXros. [All Turns] [Once Per Turn] When any of your [Xros Heart] trait Digimon are played, until the end of your opponent's turn, give 1 of their Digimon <Security A. -1> and it gets -3000 DP. [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: [When Attacking] [Once Per Turn] If this Digimon has the [Xros Heart] trait, 1 of your opponent's Digimon gets -2000 DP for the turn.
Lv.4 ShootingStarmon BT19-035 R Champion | Data | Super Major/Xros Heart [Digivolve] Lv.3 w/[Xros Heart] trait: Cost 2 This card is also treated as [Starmons] for a DigiXros. [All Turns] [Once Per Turn] When any of your [Xros Heart] trait Digimon are played, give 1 of your opponent's Digimon <Security A. -1> and it gets -3000 DP until the end of your opponent's 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: [When Attacking] [Once Per Turn] If this Digimon has the [Xros Heart] trait, 1 of your opponent's Digimon gets -2000 DP for the turn.
Lv.4 シューティングスターモン BT19-035 R 成熟期 | データ種 | 超メジャー型/クロスハート 特徴に「クロスハート」を持つLv.3:コスト2 このカードはデジクロスで「スターモンズ」としても扱う。 【お互いのターン】[ターンに1回]特徴に「クロスハート」を持つ自分のデジモンが登場したとき、相手のターン終了まで、相手のデジモン1体に≪Sアタック-1≫を与え、DP-3000。 【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: 【アタック時】[ターンに1回]このデジモンが特徴に「クロスハート」を持つなら、ターン終了まで、相手のデジモン1体をDP-2000。