Q1: Do I always have to activate this card's effect when I attack?
No, you can choose not to.
Q2: Can I activate this card's When Attacking effect if I have no cards left in my security stack?
No. If you can't add cards from your security stack to your hand, you can't activate the effect.
Q3: I attack with this Digimon, then activate its When Attacking effect to unsuspend it and give 1 of my opponent's Digimon -6000 DP. If I attack again on the same turn, can I give 1 of my opponent's Digimon an additional -6000 DP?
No. The effect has Once Per Turn, so it doesn't activate on any attacks past the first one.
Lv.6 WarGreymon BT4-048 SR Mega | Vaccine | Dragonkin [When Attacking] [Once Per Turn] You may add the top card of your security stack to your hand to unsuspend this Digimon and have 1 of your opponent's Digimon get -6000 DP for the turn.
Lv.6 WarGreymon BT4-048 SR Mega | Vaccine | Dragonkin [When Attacking] [Once Per Turn] You may add the top card of your security stack to your hand to unsuspend this Digimon and have 1 of your opponent's Digimon get -6000 DP for the turn.
Lv.6 WarGreymon BT4-048 SR Mega | Vaccine | Dragonkin [When Attacking] [Once Per Turn] You may add the top card of your security stack to your hand to unsuspend this Digimon and have 1 of your opponent's Digimon get -6000 DP for the turn.
Lv.6 ウォーグレイモン BT4-048 SR 究極体 | ワクチン種 | 竜人型 【アタック時】[ターンに1回]自分のセキュリティを上から1枚手札に加えることで、このデジモンをアクティブにし、このターンの間、相手のデジモン1体のDPを-6000する。