Q1: I attack my opponent with this Digimon. If they block it with one of their Digimon, does this card's effect activate?
Yes, it does. When Attacking effects activate before your opponent gets to activate Blocker.
Q2: If an opponent's Digimon gains Blocker from an effect or as an inherited effect from one of its digivolution cards, can I delete that Digimon with this card's effect?
Yes, you can.
Lv.6 WarGreymon EX1-009 SR Mega | Vaccine | Dragonkin [When Digivolving] <Blitz> (This Digimon can attack when your opponent has 1 or more memory.)[When Attacking] When this Digimon attacks a player, if you have a Tamer in play, delete 1 of your opponent's Digimon with <Blocker>.
Lv.6 WarGreymon EX1-009 SR Mega | Vaccine | Dragonkin [When Digivolving] <Blitz> (This Digimon can attack when your opponent has 1 or more memory.)[When Attacking] When this Digimon attacks a player, if you have a Tamer in play, delete 1 of your opponent's Digimon with <Blocker>.
Lv.6 WarGreymon EX1-009 SR mega | Vaccine | Dragonkin [When Digivolving] <Blitz>. [When Attacking] When this Digimon attacks a player, if you have a Tamer in play, delete 1 of your opponent's Digimon with <Blocker>.
Lv.6 ウォーグレイモン EX1-009 SR 究極体 | ワクチン種 | 竜人型 【進化時】≪進撃≫(メモリーが相手側の1以上のとき、このデジモンはアタックできる)【アタック時】プレイヤーにアタックしたとき、自分のテイマーがいるなら、≪ブロッカー≫を持つ相手のデジモン1体を消滅させる。