Arcana Force 0 - The Fool's second effect only concerns effects that target him. It is continuous, so,
Skill Drain will both negate The Fool's 'cannot be destroyed by battle' effect, and his own negation effect. He can be destroyed by battle now, and the opponent can target him without their effects being negated.
Divine Wrath however has to chain to activated effects. Since both of these effects are continuous, Divine Wrath can do nothing at all.
All of his effects are Triggers, which are activated effects and use the chain. You can chain Divine Wrath to any of them, to negate and destroy him.
Divine Wrath can only be used against activated effects - Obelisk has two activated effects, his destroy opposing monsters one, and the trigger that sends him to the graveyard on the turn he was special summoned. Divine Wrath can be used against either of these - note Divine Wrath does not target the monster, so Obelisk's protection effect won't stop it.
If the Tuner has an activated ability, yes, it can negate that. It cannot stop a monster 'being' a Tuner, nor affect a Synchro Summon though.
Yes, it can be used on Obelisk's activated effects (Divine Wrath does not target) and most of the time, Ra's Ignition Effect effect, but when Ra summons itself, no effect apart from its own can be used in the response chain. So if Ra uses its Trigger or Ignition Effect in response to its own summon, Divine Wrath can't be used against it.
Prime Material Dragon has an activated effect that can chain to and negate destruction effects. If it ever uses this effect, Divine Wrath can be chained to it, and Prime Material Dragon will be negated and destroyed, meaning the original destruction effect resolves correctly. Note that as a Quick Effect, Prime Material Dragon is unable to save itself from spell speed 3 destruction cards like Divine Wrath. Note also that Prime Material's effect to change direct damage into lifegain, is continuous and Divine Wrath can't be used against it.
All of his effects are Triggers, which are activated effects and use the chain. You can chain Divine Wrath to any of them, to negate and destroy him.
Divine Wrath can only be used against activated effects - Obelisk has two activated effects, his destroy opposing monsters one, and the trigger that sends him to the graveyard on the turn he was special summoned. Divine Wrath can be used against either of these - note Divine Wrath does not target the monster, so Obelisk's protection effect won't stop it.
Yes, the monster effect is still being activated whether it is on the field or not.
Mirage Dragon's effect is continuous and can't be chained to. No activation means no Divine Wrath, Divine Wrath can only be used against activated monster effects.
No, you can use Divine Wrath on your own activated monster effects if you wish. Just as long as it is indeed an effect that activates and therefore uses the chain.
Divine Wrath can be used against monster effects that activate. Marshmallon has an activated effect that deals damage, Man Eater Bug has an activated effect, as does Penguin Soldier. All can be stopped with Divine Wrath. Marshmallon also has a continuous effect that stops it being destroyed by battle, and Cyber Dragon has an inherent special summon effect. Neither of these activate, so Divine Wrath can't be used against them.
Yes, you can do this. When Divine Wrath resolves and tries to destroy Thought Ruler Archfiend, you can pay 500 LP and destroy Telekinetic Shocker's effect instead.
Firstly, Stardust Dragon can only negate effects that destroy cards on the field. Secondly, Exodia the Forbidden One's effect is not something that is activated, the game ends immediately. You cannot stop it with cards like Divine Wrath, etc. In other words it connot be stopped by any card.
Divine Wrath is a counter trap. When a monster's effect activates (therefore it cannot be used against an effect that does not 'activate') you can chain it by discarding one card. When Divine Wrath resolves, the monster's activation and effect is negated, and the monster is destroyed. The monster does not have to be in hand for Divine Wrath to be used, it can stop them no matter which zone they are in, as long as it is indeed an activated effect.
hmm, how to explain that in lamens terms... It means that some divine power (IE: god) created the cosmos(created not developed); meaning that the cosmos was already in the state it is now when that divine power created it. IE: If the cosmos was 20,000,000 years old and the divine power created it 20,000 years ago, it would mean that the cosmos the divine power created would already be 19,980,000 years old (right out of the box - no assembly - kindof concept).
If the Tuner has an activated ability, yes, it can negate that. It cannot stop a monster 'being' a Tuner, nor affect a Synchro Summon though.
Yes, it can be used on Obelisk's activated effects (Divine Wrath does not target) and most of the time, Ra's Ignition Effect effect, but when Ra summons itself, no effect apart from its own can be used in the response chain. So if Ra uses its Trigger or Ignition Effect in response to its own summon, Divine Wrath can't be used against it.