Q1: What does the "your opponent can't gain memory other than by Tamer effects" effect do, exactly?
With this effect, your opponent's memory will no longer increase by any effects except Tamer effects. This effect affects the opponent player.
Q2: Can I use the All Turns effect on BT17-087 Marcus Damon to gain memory if it's treated as a Digimon and suspends while my opponent has "your opponent can't gain memory other than by Tamer effects" activated?
Yes, you can gain memory. When an effect is activated on a card that's treated as both a Digimon and a Tamer, the effect is treated as both a Digimon effect and a Tamer effect, therefore you can gain memory.
Lv.3 Shamanmon BT18-009 C Rookie | Virus | Demon [All Turns] Your opponent can't gain memory other than by Tamer effects.
Lv.3 Shamanmon BT18-009 C Rookie | Virus | Demon [All Turns] Your opponent can't gain memory other than by Tamer effects.
Lv.3 Shamanmon BT18-009 C Rookie | Virus | Demon [All Turns] Your opponent can't gain memory except with Tamer effects.
Lv.3 シャーマモン BT18-009 C 成長期 | ウィルス種 | 鬼人型 【お互いのターン】相手はテイマーの効果以外でメモリーをプラスできない。