Yes. Royal Decree only negates the resolutions, it does not negate nor prevent activations.
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.
It is an Ignition Effect, so can only be activated in your turns.
Yes, the effect only works after the effect resolves, so you can activate it in a chain to "Royal Decree". Cards like "Dust Tornado" can even destroy "Royal Decree" as it is chained to "Royal Decree"'s activation. When the chain resolves, "Dust Tornado" will destroy "Royal Decree" and "Royal Decree"'s effect will disappear since it is no longer on the field.
Yes, being targetted in no way 'locks' the targetted card, stopping it from being activated. If it's the correct spell speed, it can be activated in chain to the targeting effect.
Yes. The chain will finish resolving first of all, summoning your Fusion Monster. Elemental Hero Absolute Zero's effect will then activate, destroying your Fusion Monster unless you have a way to save it.
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.
Peten's effect is an Optional Trigger ('you can') which have a restriction on when they can activate. If their condition is met, but something resolves, or is summoned, before they can activate, then they miss the timing and do not activate. So with Peten, if he is tributed for any kind of cost, including tribute summon, then the monster's summon or resolving effect make him miss the timing. It is important to note that other activations alone do not make a card miss the timing, nor can a correctly activated Optioal Trigger subsequently miss the timing. It is a resolution before the optional trigger can activate that does it. For example Giant Rat's effect is Optional, if two battle and destroy each other, their effects will form a chain with each other. Nothing happened in between the condition being met, so both activated legally, one's resolution does not prevent the other resolving.
No, it is an Ignition Effect and can only be activated on your own turns.
It is an Ignition Effect, so can only be activated in your turns.
Yes, the effect only works after the effect resolves, so you can activate it in a chain to "Royal Decree". Cards like "Dust Tornado" can even destroy "Royal Decree" as it is chained to "Royal Decree"'s activation. When the chain resolves, "Dust Tornado" will destroy "Royal Decree" and "Royal Decree"'s effect will disappear since it is no longer on the field.
No. A card cannot be activated, if it is unable to resolve. Cards like Statue of the Wicked and Ojamagic, do not have a resolvable effect that can occur from activating them on the field. All their effects are triggers, which activate under other circumstances. Because nothing would resolve, they can't even be activated on the field. Ojamagic's effect only triggers after it leaves the field, so there'd still be no resolvable effect from trying to activate it on the field.
No. Wind-Up Rat's effect is targeted and can't be activated if there's no valid target.
'Activation' and 'resolution' should not be confused, activation is when the card is turned face up, and resolution is when the effect is applied. After you activate a card like Mirror Force, it does not matter what happens to the physical card itself later on in the chain - it could be destroyed by Twister, or sent to the graveyard for Emergency Provisions, for example. Neither of these will stop the effect (which has already been activated) from resolving. To stop the effect from resolving, you have to use a card that says it negates the effect of the trap, so cards like Solemn Judgment or Seven Tools of the Bandit have to be used - just destroying the card is not enough.
No, it triggers in response to the declaration of the attack. If it is face down at this point, then it misses its chance to activate. When it is flipped face-up at the beginning of the Damage Step, it is too late to use its effect.
Shuttleroid's trigger has to be activated in response to an attack declaration against it. If it is face-down at the time, it can't activate the effect. When it flips face-up at the beginning of the Damage Step, then it is past the point when it could activate.
Yes, that particular Quick Effect can be activated in the Damage Step.
Tyrant's Tantrum can only be activated once, you pay the cost to flip it face-up and then it just remains face-up on the field applying its effect. It does not have a reusable effect that can be repeatedly activated such as Royal Oppression.