Gomamon

Q:What does the "your opponent can't gain memory other than by Tamer effects" effect do, exactly?

A:With this effect, your opponent's memory will no longer increase by any effects except Tamer effects. This effect affects the opponent player.

Q:Can I gain memory using an effect on a Tamer that's treated as a Digimon with X000 DP due to an effect while my opponent has "your opponent can't gain memory other than by Tamer effects" activated?

A:Yes, you can. 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.