Q2: Do I have to attack with Blitz to get Security Attack +1 from this card's inherited effect?
No. As long as the Digimon this card is a digivolution card in has Blitz, it gains Security Attack +1, regardless of whether it attacks or not.
Q3: Can I digivolve one of my Shoutmon in the battle area into this card in the hand when an effect to digivolve one of my Digimon is activated?
Yes, you can.
Lv.5 OmniShoutmon BT5-014 R Ultimate | Data | Dragonkin Your [Shoutmon] can digivolve into this card in your hand for a memory cost of 4, ignoring this card's digivolution requirements. --- Inherited: [Your Turn] While this Digimon has <Blitz>, it gains <Security Attack +1>. (This Digimon checks 1 additional security card.)
Lv.5 OmniShoutmon BT5-014 R Ultimate | Data | Dragonkin Your [Shoutmon] can digivolve into this card in your hand for a memory cost of 4, ignoring this card's digivolution requirements. --- Inherited: [Your Turn] While this Digimon has <Blitz>, it gains <Security Attack +1>. (This Digimon checks 1 additional security card.)
Lv.5 OmniShoutmon BT5-014 R Ultimate | Data | Dragonkin Your [Shoutmon] can digivolve into this card in your hand for a memory cost of 4, ignoring this card's digivolution requirements. --- Inherited: [Your Turn] While this Digimon has <Blitz>, it gains <Security A. +1>.
Lv.5 オメガシャウトモン BT5-014 R 完全体 | データ種 | 竜人型 自分の「シャウトモン」は手札のこのカードに進化条件を無視して進化コスト4で進化できる。 --- Inherited: 【自分のターン】このデジモンが≪進撃≫を持つ間、このデジモンは≪セキュリティアタック+1≫(このデジモンがチェックするセキュリティの枚数+1)を得る。