Tentomon

Q:What does a "your opponent can't reduce digivolution costs" effect do, exactly?

A:This effect prevents digivolution costs from being reduced when the costs are to be paid. This effect affects the opponent player.

Q:Can my opponent digivolve a card using a "digivolve without paying the cost" effect while a "your opponent can't reduce digivolution costs" effect is activated?

A:Yes, it can be digivolved. "Digivolve without paying the cost" effects aren't effects that reduce the digivolution cost.