This effect prevents costs from being reduced when play costs are to be paid. This effect affects both players.

Yes, you can. "Play this card without paying the cost" effects aren't effects that reduce the play cost.

No, play costs can't be reduced. A "players can't reduce play costs" effect isn't an effect that affects cards that activate play-cost-reducing effects, it's an effect that affects players. Therefore, the target players can't reduce play costs.

Yes, DigiXrosing is possible. However, it isn't possible to reduce play costs through DigiXrosing. Therefore, a player can't declare to play a card in a state where its play cost can't be paid.