No, Dust Tornado is a destruction card but not a negation card.
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No, she doesn't 'negate' it. She protects your other face-up Lv3 or lower Zombies from being affected by Spells or Traps, but does not negate the effect itself.
No monster can chain to a Counter Trap in order to negate the activation. Quick monster effects are spell speed 2, and only Counter Traps can chain to Counter Traps, spell speed 3. So cards like Light and Darkness Dragon and Stardust Dragon can't be used against them. Some monsters can prevent the activation of Counter Traps such as Jinzo. A few others have continuous effects that negate all trap effects. Sky Scourge Invicil is one, when summoned with a Dark monster as tribute.
No. Slifer the Sky Dragon's Normal Summon can't be negated, and cards/effects cannot be used in response to its Normal Summon. However apart from that it has no other protection, it cannot negate anything.
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.
Yes, Slifer and any other Egyptian God card can be destroyed by trap cards. More specifically, traps that don't target, like "Mirror Force", and traps that negate effects and destroy, like "Divine Wrath".