

Q1: If this card's On Play When Digivolving effect couldn't suspend a Digimon, does that mean it can't give that Digimon "can't unsuspend"?
No, even if this effect didn't suspend the target, it can still give it "can't unsuspend."
Q2: In what order do a Security effect, "when ... performs a security check" effect, and "when a card is removed from ... security stack" effect activate when they trigger simultaneously upon a security check?
Security effects take precedence for activation. Upon a check, a Security effect will immediately activate without pending activation. For other triggered effects, the turn player activates their effects first.
Lv.5 Aegiochusmon: Green BT25-053 R Ultimate | Vaccine | Shaman/Iliad/TS <Vortex> <Decode ([Aegiomon])> [On Play] [When Digivolving] Suspend 1 of your opponent's Digimon or Tamers. It can't unsuspend until their turn ends. Then, if you have 3 or fewer security cards, this Digimon gains <Piercing> and +5000 DP for the turn. (Rule) Trait: Has [Vegetation] Type. --- [All Turns] [Once Per Turn] When your security stack is removed from, you may suspend 1 of your opponent's Digimon or Tamers.
Lv.5 Aegiochusmon: Green BT25-053 R Ultimate | Vaccine | Shaman/Iliad/TS [Digivolve] [Aegiomon]: Cost 3 <Vortex> <Decode ([Aegiomon])> [On Play] [When Digivolving] Suspend 1 of your opponent's Digimon or Tamers. It can't unsuspend until their turn ends. Then, if you have 3 or fewer security cards, this Digimon gains <Piercing> and +5000 DP for the turn. (Rule) Trait: Has [Vegetation] Type. --- [All Turns] [Once Per Turn] When your security stack is removed from, you may suspend 1 of your opponent's Digimon or Tamers.
Lv.5 Aegiochusmon: Green BT25-053 R ultimate | Vaccine | Shaman/Iliad/TS [Digivolve] [Aegiomon]: Cost 3 <Vortex> <Decode ([Aegiomon])> [On Play] [When Digivolving] Suspend 1 of your opponent's Digimon or Tamers. It can't unsuspend until their turn ends. Then, if you have 3 or fewer security cards, this Digimon gains <Piercing> and +5000 DP for the turn. (Rule) Trait: Has [Vegetation] Type. --- [All Turns] [Once Per Turn] When your security stack is removed from, you may suspend 1 of your opponent's Digimon or Tamers.
Lv.5 アイギオテュースモン:グリーン BT25-053 R 完全体 | ワクチン種 | 神人型/イリアス/TS ≪ヴォルテクス≫≪デコード《「アイギオモン」》≫ 【登場時】【進化時】相手のデジモン/テイマー1体をレストさせる。相手のターン終了まで、そのデジモン/テイマーはアクティブにならない。その後、自分のセキュリティが3枚以下なら、ターン終了まで、このデジモンは≪貫通≫を得て、DP+5000。 〈ルール〉特徴:タイプ「植物型」を持つ。 --- 【お互いのターン】[ターン1回]自分のセキュリティが減ったとき、相手のデジモン/テイマー1体をレストできる。