As a Spell Speed 2 card, you cannot chain Royal Decree to a Counter Trap. However if Royal Decree is already active, any Counter Traps that try to resolve, will be negated.
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You can still activate them, but Royal Decree negates all other traps except itself, so they will be negated. You can however activate such a card like Seven Tools of The Bandit to negate the activation of Royal Decree itself and destroy it, because Royal Decree does not apply the negation effect until it resolves.
Trap Stun, Royal Decree.
'Negation' can have two different contexts. You can negate a card's activation (meaning the resolution never happens) or just negate the effect (meaning it resolves but does nothing). Solemn Judgment can negate activations, Royal Decree negates resolutions, and also switches off the effects of continuous traps.If you negate the activation or the effect of Normal Traps and Counter Traps, then that means you don't get their effect. If the negation effect destroys them, they will go to the graveyard on destruction, otherwise they will go to the graveyard when the chain finishes resolving.If you negate the activation of a continuous Trap card, then it is unable to remain on the field, and it will go to the graveyard.If you negate the effect of a continuous Trap card, then it will be able to stay on the field, however will do nothing until the negation effect ends. So if it was an active Royal Decree that was negating it, its effects will become active again if Royal Decree leaves the field. This goes for both chaining a negation effect to the activation of the continuous trap, or activating one later on, while the continuous trap is face-up and active.
Yes. Royal Decree only negates the resolutions, it does not negate nor prevent activations.
Jinzo, Royal Decree and Trap Stun negate the effects, Trap Jammer, Solemn Judgment, Seven Tools of the Bandit negate both activation and effect.