Q1: Which player chooses the Digimon to suspend with this card's skill?
The player who controls this card chooses.
Q2: My opponent attacks with a Digimon that has a When Attacking effect that suspends an opponent's Digimon, and uses it to suspend one of my unsuspended Digimon. When they do, does this card's effect activate?
Yes, it does. If your opponent attacks you with a Digimon, if this Digimon is suspended, its effect can be activated at counter timing even if it it was unsuspended when the attack was declared.
Q3: This Digimon has Blocker and is currently unsuspended when my opponent attacks with a Digimon. If I suspend this Digimon to block the opponent's Digimon, can I activate this card's effect to suspend one of my opponent's Digimon?
No, you can't. This Digimon's Opponent's Turn effect triggers at counter timing, before a block can be declared with Blocker at blocker timing. So, if this Digimon is not suspended during the counter timing, you can't activate this Digimon's Opponent's Turn effect.
Lv.6 Rosemon BT1-082 SR Mega | Data | Fairy [Opponent's Turn] When an opponent's Digimon attacks a player, if this Digimon is suspended, suspend 1 of your opponent's Digimon.
Lv.6 Rosemon BT1-082 SR Mega | Data | Fairy [Opponent's Turn] When an opponent's Digimon attacks a player, if this Digimon is suspended, suspend 1 of your opponent's Digimon.
Lv.6 Rosemon BT1-082 SR Mega | Data | Fairy [Opponent's Turn] When an opponent's Digimon attacks a player, if this Digimon is suspended, suspend 1 of your opponent's Digimon.
Lv.6 ロゼモン BT1-082 SR 究極体 | データ種 | 妖精型 【相手のターン】相手のデジモンがプレイヤーにアタックしたとき、このデジモンがレスト状態なら、相手のデジモン1体をレストさせる。