Q1: What does "players can't reduce play costs" mean, exactly?

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

Q2: What does "players can't reduce play costs" effect has activated?

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

Q3: What does "players can't reduce play costs" effect has activated?

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.

Q4: What does "players can't reduce play costs" effect has activated?

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.