

Q1: If an effect reads "All Turns While this Digimon is suspended, it gets +1000 DP," and 12000 DP when it attacks, does this card's All Turns effect trigger?
Yes, it triggers. The suspending and the timing for getting +1000 DP are the same, therefore the All Turns effect triggers.
Q2: Can I activate this card's All Turns effect even when a Digimon with 12000 DP or less attacks and a When Attacking effect causes its DP to become 13000 DP or more?
No, you can't. It won't trigger if the DP is 12000 or less upon the attack.
Q3: Does this card's All Turns effect trigger when either my Digimon or my opponent's Digimon attacks?
Yes, it triggers.
Lv.5 GrapLeomon BT25-016 R Ultimate | Vaccine | Beastkin/Iliad/TS [On Play] [When Digivolving] 1 of your Digimon gets +3000 DP for the turn. Then, 1 of your Digimon may attack. [All Turns] When a Digimon with 13000 DP or more attacks, this Digimon may digivolve into [Marsmon] or [Callismon] in the hand without paying the cost. --- <Security A. +1> (This Digimon checks 1 additional security card.)
Lv.5 GrapLeomon BT25-016 R Ultimate | Vaccine | Beastkin/Iliad/TS [Digivolve] Lv.4 w/[TS] trait: Cost 3 [On Play] [When Digivolving] 1 of your Digimon gets +3000 DP for the turn. Then, 1 of your Digimon may attack. [All Turns] When a Digimon with 13000 DP or more attacks, this Digimon may digivolve into [Marsmon] or [Callismon] in the hand without paying the cost. --- <Security A. +1> (This Digimon checks 1 additional security card.)
Lv.5 GrapLeomon BT25-016 R ultimate | Vaccine | Beastkin/Iliad/TS [Digivolve] Lv.4 w/[TS] trait: Cost 3 [On Play] [When Digivolving] 1 of your Digimon gets +3000 DP for the turn. Then, 1 of your Digimon may attack. [All Turns] When a Digimon with 13000 DP or more attacks, this Digimon may digivolve into [Marsmon] or [Callismon] in the hand without paying the cost. <Security A. +1>
Lv.5 グラップレオモン BT25-016 R 完全体 | ワクチン種 | 獣人型/イリアス/TS 【登場時】【進化時】ターン終了まで、自分のデジモン1体をDP+3000。その後、自分のデジモン1体でアタックできる。 【お互いのターン】DP13000以上のデジモンがアタックしたとき、このデジモンを手札の「マルスモン」/「カリスモン」にコストを支払わず進化できる。 --- ≪Sアタック+1≫(このデジモンがチェックする枚数+1)