

Q1: Can this card's On Play When Digivolving effect give "can't unsuspend" to a card that was not suspended by it?
Yes, it can.
Lv.5 Lilamon BT26-044 U Ultimate | Data | Fairy/DATA SQUAD [On Play] [When Digivolving] You may suspend 1 of your opponent's Digimon or Tamers. Then, 1 of their Digimon or Tamers can't unsuspend until their turn ends. [Your Turn] [Once Per Turn] When any of your opponent's Digimon or Tamers suspend, or effects trash cards from under your Tamers, this Digimon may digivolve into a [Vegetation], [Fairy] or [DATA SQUAD] trait Digimon card in the hand with the cost reduced by 1. --- [All Turns] [Once Per Turn] When this Digimon with [Rosemon] in its name or the [DATA SQUAD] trait would leave the battle area, by trashing the bottom face-down card from under any of your Tamers, it doesn't leave.
Lv.5 Lilamon BT26-044 U Ultimate | Data | Fairy/DATA SQUAD [Digivolve] Lv.4 w/[DATA SQUAD] trait: Cost 3 [On Play] [When Digivolving] You may suspend 1 of your opponent's Digimon or Tamers. Then, 1 of their Digimon or Tamers can't unsuspend until their turn ends. [Your Turn] [Once Per Turn] When any of your opponent's Digimon or Tamers suspend, or effects trash cards from under your Tamers, this Digimon may digivolve into a [Vegetation], [Fairy] or [DATA SQUAD] trait Digimon card in the hand with the cost reduced by 1. --- [All Turns] [Once Per Turn] When this Digimon with [Rosemon] in its name or the [DATA SQUAD] trait would leave the battle area, by trashing the bottom face-down card from under any of your Tamers, it doesn't leave.
Lv.5 Lilamon BT26-044 U ultimate | Data | Fairy/DATA SQUAD [Digivolve] Lv.4 w/[DATA SQUAD] trait: Cost 3 [On Play] [When Digivolving] You may suspend 1 of your opponent's Digimon or Tamers. Then, 1 of their Digimon or Tamers can't unsuspend until their turn ends. [Your Turn] [Once Per Turn] When any of your opponent's Digimon or Tamers suspend, or effects trash cards from under your Tamers, this Digimon may digivolve into a [Vegetation], [Fairy] or [DATA SQUAD] trait Digimon card in the hand with the cost reduced by 1. --- [All Turns] [Once Per Turn] When this Digimon with [Rosemon] in its name or the [DATA SQUAD] trait would leave the battle area, by trashing the bottom face-down card from under any of your Tamers, it doesn't leave.
Lv.5 ライラモン BT26-044 U 完全体 | データ種 | 妖精型/セイバーズ 【登場時】【進化時】相手のデジモン/テイマー1体をレストできる。その後、相手のターン終了まで、相手のデジモン/テイマー1体はアクティブにならない。 【自分のターン】[ターン1回]相手のデジモン/テイマーがレストしたときか、自分のテイマーの下のカードが効果で破棄されたとき、このデジモンを手札の特徴「植物型」/「妖精型」/「セイバーズ」を持つデジモンカードに支払うコスト-1で進化できる。 --- 【お互いのターン】[ターン1回]名称に「ロゼモン」を含むか特徴「セイバーズ」を持つこのデジモンがバトルエリアを離れるとき、自分のテイマーの下にある裏向きのカードを下から1枚破棄することで、離れない。