Q1: Can either my Digimon or my opponent's Digimon be specified for the Digimon that are suspended and unsuspended by this card's When Digivolving effect?
Yes, they can. This effect doesn't specify a player, so you can specify either player's Digimon as the effect's targets.
Q2: Does this card's All Turns effect trigger when either my Digimon or my opponent's Digimon is unsuspended?
Yes, it triggers. It triggers regardless of which player's Digimon is unsuspended.
Lv.6 Zephagamon ST18-12 SR Mega | Magic Knight/Vortex Warriors/LIBERATOR <Vortex> (At the end of your turn, this Digimon may attack an opponent's Digimon. With this effect, it can attack the turn it was played.) [When Digivolving] Suspend 1 Digimon. Then, unsuspend 1 Digimon. [All Turns] [Once Per Turn] When any Digimon unsuspend, for the turn, this Digimon isn't affected by the effects of your opponent's Digimon and gets +3000 DP. (Rule) Trait: Has [Bird Dragon] Type.
Lv.6 Zephagamon ST18-12 SR Mega | Data | Magic Knight/Vortex Warriors/LIBERATOR <Vortex> (At the end of your turn, this Digimon may attack an opponent's Digimon. With this effect, it can attack the turn it was played.) [When Digivolving] Suspend 1 Digimon. Then, unsuspend 1 Digimon. [All Turns] [Once Per Turn] When any Digimon unsuspend, for the turn, this Digimon isn't affected by the effects of your opponent's Digimon and gets +3000 DP. (Rule) Trait: Has [Bird Dragon] Type.
Lv.6 Zephagamon ST18-12 SR Mega | Data | Magic Knight/Vortex Warriors/LIBERATOR <Vortex> [When Digivolving] Suspend 1 Digimon. Then, unsuspend 1 Digimon. [All Turns] [Once Per Turn] When any Digimon unsuspend, for the turn, this Digimon isn't affected by the effects of your opponent's Digimon and gets +3000 DP. (Rule) Trait: Has [Bird Dragon] type.
Lv.6 ゼファーガモン ST18-12 SR 究極体 | データ種 | 魔法騎士型/ヴォルテクスウォリアー/リベレイター ≪ヴォルテクス≫(自分のターン終了時、このデジモンで相手のデジモンにアタックできる。この効果では、登場したターンでもアタックできる) 【進化時】デジモン1体をレストさせる。その後、デジモン1体をアクティブにする。 【お互いのターン】[ターンに1回]デジモンがアクティブになったとき、ターン終了まで、このデジモンは相手のデジモンの効果を受けず、DP+3000。 〈ルール〉特徴:タイプ「鳥竜型」を持つ。