Q1: Do I gain 1 memory for each Digimon my opponent has without digivolution cards?
No. You only gain 1 memory no matter how many Digimon your opponent has without digivolution cards.
Q2: Does this Tamer's effect apply if my opponent has a Digimon with no digivolution cards in their breeding area?
No, it doesn't check Digimon in the breeding area.
Q3: Does this Tamer's effect apply when my opponent has no Digimon in their battle area?
No, it doesn't. Your opponent has to have a Digimon in their battle area for it to activate.
Q4: If I have two of this Tamer in play and my opponent has a Digimon with no digivolution cards, do I gain 2 memory from this Tamer's effect?
Yes. The effect of each copy activates, causing you to gain 2 memory.
Matt Ishida ST2-12 R [Start of Your Turn] If your opponent has a Digimon with no digivolution cards, gain 1 memory. --- [Security] Play this card without paying its memory cost.
Yamato Ishida ST2-12 R [Start of Your Turn] If your opponent has a Digimon with no digivolution cards, gain 1 memory. --- [Security] Play this card without paying its cost.
Matt Ishida ST2-12 R [Start of Your Turn] If your opponent has a Digimon with no Digivolution cards, gain 1 memory. ---
石田ヤマト ST2-12 R 【自分のターン開始時】進化元を持たない相手のデジモンがいるとき、メモリーを+1する。 --- 【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。