Yes. It doesn't matter what zone the monster is in, Divine Wrath can be used against it as long as it 'activates'.
It doesn't matter that Divine Wrath is unable to apply a destruction effect due to the monster being in the graveyard, that's not a condition of activation.
The monster will always return to its owner's Graveyard. Incidentally, if the effect of the destroyed monster activates while it is still on the field, you will be able to use it; however, if the effect activates in the Graveyard, the card's owner will control the effect.
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.
As a matter of fact, yes. The end of Anubis does negate Stardust Dragon's effect as long as he is on the field. Since Stardust Dragon's effect activates in the graveyard, and The End of Anubis' effect states "Monster cards that designate a card(s) in the graveyard or activate in the graveyard are negated."
Totem Dragon only has one effect that activates, the one that can special summon itself. If there are other monsters in the graveyard, that are non-Dragon types, then this effect cannot be activated.
No, it can't negate either of its effects. Skill Drain only negates a monster's resolution if the monster card is face-up on the field when it tries to resolve. With Stardust Dragon, its negation effect activates on the field but sends itself to the graveyard as a cost. Skill Drain can't touch it there. It's resummoning effect activates in the graveyard, so again, Skill Drain can't stop it.
No, Divine Wrath must chain to a monster effect when it activates. Buster Blader's ATK increasing effect is continuous, it never 'activates', at no point does it ever use the chain, even when it is summoned, or the ATK changes. Because it is continuous, Divine Wrath cannot be used against it.
No, it only works if wall of illusion is attacked, even if wall of illusion is destroyed after being attacked the effect still activates.
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.
No, it is NEVER the same. The two terms are totally different, even if yes, it involves sending a monster from the field to graveyard. But if a monster says it activates an effect when it is destroyed, it will never activate from a tribute.
Yes because it's effect says you can summon a normal dragon type monster from either players graveyard. So since tribute to the doom destroys the monster is effect activates.
The effect activates first, and you are actually chaining Trap Hole to that trigger. Trap Hole will resolve first, but it will not stop the monster effect from resolving. Unless a card says it negates a monster's effect, then it is still able to resolve its affect when flip summoned.
If a monster activates an effect, then Fiendish Chain can be chained to this. Fiendish Chain will resolve first, meaning the monster's effect will be negated when it tries to resolve. So if Chaos Sorcerer activates his Ignition Effect, Fiendish Chain can be used to negate it.