It negates effects that read, “reduce the play cost by X.” When you or your opponent activates an effect like that, it won't reduce the play cost that needs to be paid. The full play cost of the card needs to be paid.

Yes, "Play this card without paying the cost" effects are not effects that reduce the play cost, so they can activate.

No, they can't be reduced. This card's effect does not target Digimon, so even if your opponent's [BT13-007 King Drasil_7D6] is in the breeding area, its effect to reduce play costs can't be activated.

That's correct. Such effects can no longer reduce play costs. This card's effect also prevents play cost-reducing effects from activating when Tamer cards are played.