No, she can only negate Spell, Trap or Monster effects that Target. Dark Hole does not target anything.
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Sometimes it can, sometimes it can't. Stardust Dragon says;"You can Tribute this card to negate the activation of a Spell Card, Trap Card, or Effect Monster's effect that destroys a card(s) on the field, and destroy that card."Tytannial says;"You can Tribute 1 face-up Plant-Type monster you control to negate the activation of a Spell, Trap, or Effect Monster's effect that targets a card(s) on the field and destroy it."Stardust Dragon can only negate effects that will destroy a card on the field - and while Tytannial can certainly negate and destroy cards like that, her effect can be used against cards that are not on the field too. She only cares about the location of the target, not the location of the effect.So, a few examples.Player A uses Snipe Hunter, picking a target. Because it is a targetted effect, Tytannial can chain to this with her negation effect. Because her effect will be destroying a card on the field, Stardust Dragon can use its negation effect against her.Player A uses Exiled Force, picking a target. Because it is a targetted effect, Tytannial can chain to this with her negation effect. However, since Exiled Force goes to the graveyard as a cost, Tytannial will not be destroying a monster on the field. Stardust Dragon is unable to chain with its negation effect.
Bottomless Trap Hole does not target, so Tyrant Dragon is unable to negate it.
You cannot activate Trap Hole to negate the tribute summon of Jinzo in Yu-Gi-Oh. No effect of Trap Hole can be activated because Jinzo negates traps in the game. However, your only option to totally prevent Jinzo from negating trap card effects is to negate his summon. To negate a monster's summon also prevents any of its effects on the field from applying. Cards like Solemn Warning not only negate the summoning of a monster but also prevent its effects on the field from ever applying and also destroys the monster.
It will negate Trap Hole, but not Sakuretsu Armor. Sakuretsu Armor is most definitely a card that targets, however when Ancient Gear Engineer attacks, the opponent cannot use Spells or Traps until the end of the Damage Step. That means he could not respond to the attack with Sakuretsu Armor in the first place.
No. No part of Bottomless Trap Hole negates effects. However a monster's continuous effect requires it to remain face-up on the field. In those cases, the monster effect will cease to apply as the monster is gone.