Rulings
Q1: Can I use this card's All Turns effect to gain 2 memory if I have a Digimon with {{EffectLinkArchetype|Greymon}} and a Digimon with {{EffectLinkArchetype|Garurumon}}?
Yes, that's correct.
Q2: When I play a Digimon with {{EffectLinkArchetype|Greymon|Garurumon}}, then its DP becomes 0 and is deleted upon play due to a persistent effect, can I activate this card's All Turns effect?
Yes, you can. Even if the played Digimon is removed before the effect activates, it triggers because the "when ... Digimon is played" condition is met, then the effect can activate. However, the "if you have a Digimon with {{EffectLinkArchetype|XX}}" condition is no longer met once the Digimon is removed, therefore you don't gain 1 memory.
Q3: Can I use this card's End of Your Turn effect to attack using my Digimon with {{EffectLinkArchetype|Omnimon}} even when it's suspended?
No, you can't. This card's End of Your Turn effect does not allow you to attack with Digimon that are in a state where they can't attack.
Q4: I attacked using BT5-086 Omnimon's Blitz and unsuspended it using the other When Digivolving effect. After the attack ends, can I use this card's End of Your Turn effect to attack again?
Yes, you can. If BT5-086 Omnimon digivolves during the main phase, you can use the End of Your Turn effect to attack again after the attack from Blitz ends.
Q5: When I have 2 copies of this Tamer and 2 unsuspended Digimon with {{EffectLinkArchetype|Omnimon|text=in their names}}, can I activate the End of Your Turn effect on both copies of this card and attack using both of the Digimon with {{EffectLinkArchetype|Omnimon|text=in their names}}?
No, you can't. The effect will trigger on both copies, but after the attack declaration is made for the 1st Omnimon and effects such as When Attacking effects have finished activating, the effect on the 2nd copy of this card that was pending activation will activate before the counter timing. However, a new attack declaration can't be made during an attack, and only the 1st Omnimon's attack can be performed as a result.
Data Sources
Tai Kamiya & Matt Ishida BT17-081 R [All Turns] When one of your Digimon is played or digivolves, by suspending this Tamer, if you have a Digimon with [Greymon] in its name, gain 1 memory. If you have one with [Garurumon] in its name, gain 1 memory. [End of Your Turn] [Once Per Turn] 1 of your Digimon with [Omnimon] in its name may attack a player. --- [Security] Play this card without paying the cost.
Tai Kamiya & Matt Ishida BT17-081 R [All Turns] When one of your Digimon is played or digivolves, by suspending this Tamer, if you have a Digimon with [Greymon] in its name, gain 1 memory. If you have one with [Garurumon] in its name, gain 1 memory. [End of Your Turn] [Once Per Turn] 1 of your Digimon with [Omnimon] in its name may attack a player. --- [Security] Play this card without paying the cost.
Tai Kamiya & Matt Ishida BT17-081 R [All Turns] When one of your Digimon is played or digivolves, by suspending this Tamer, if you have a Digimon with [Greymon] in its name, gain 1 memory. If you have a Digimon with [Garurumon] in its name, gain 1 memory. [End of Your Turn] [Once Per Turn] 1 of your Digimon with [Omnimon] in its name may attack a player. --- [Security] Play this card without paying the cost.
八神太一＆石田ヤマト BT17-081 R 【お互いのターン】自分のデジモンが登場/進化したとき、このテイマーをレストさせることで、名称に「グレイモン」を含む自分のデジモンがいるなら、メモリー+1。名称に「ガルルモン」を含む自分のデジモンがいるなら、メモリー+1。 【自分のターン終了時】[ターンに1回]名称に「オメガモン」を含む自分のデジモン1体でプレイヤーにアタックできる。 --- 【セキュリティ】このカードをコストを支払わずに登場させる。