Yes it can. 'Des Croaking' is an effect that will destroy monsters on the field, therefore Prime Material Dragon can chain to and negate it.
Yes, it can. Dark Hole is an effect that destroys monsters on the field, so Prime Material Dragon can negate it.
Yes. Gandora's Ignition Effect is a destruction effect, so you can chain Stardust Dragon to it, to negate and destroy it.
Yes it can. Sangan is a triggered effect, Stardust Dragon Assault Mode can chain to and negate it.
Because Dark End Dragon does not 'destroy' anything, Stardust Dragon is unable to negate it.
No, you either negate the entire effect with Prime Material Dragon or get rid of all of the monsters on the field. You cannot simply choose which monsters gets to be destroyed. You cannot negate an effect midway during its resolution.
Stardust Dragon has a triggered effect that special summons it from the graveyard on the turn that it negated an opponent's effect. Forbidden Graveyard will negate this trigger, Stardust Dragon will not be summoned.
Prime Material Dragon's effect has to be chained to whatever you want it to negate. So if Dark Hole is activated, it has to chain to it, to negate it. If you allow Dark Hole to resolve, all monsters will be destroyed, including Prime Material Dragon. There is no way to only let Dark Hole destroy some monsters and then be prevented from destroying others in that way.
If an opponent activates a card effect from their hand, "Majestic Star Dragon" can negate and destroy it. For example, if your opponent activates the effect of "Honest" from their hand to boost their monster's ATK, you can chain to the effect with "Majestic Star Dragon" to negate and destroy "Honest" and its effect.
Prime Material Dragon's negation effect is a Quick Effect. Even though Gladiator Beast War Chariot is a destruction effect, PMD's spell speed 2 effect is not able to chain to counter traps, which are spell speed 3.
Prime Material Dragon's negation effect is a Quick Effect. Even though Gladiator Beast War Chariot is a destruction effect, PMD's spell speed 2 effect is not able to chain to counter traps, which are spell speed 3.
Yes, if a card effect activating from the Graveyard will destroy a monster, Spell, or Trap card "Stardust Dragon" can be activated to negate the effect. Even though "Stardust Dragon" states that it destroys and negates cards, it can still negate an effect resolving in the Graveyard; the card in the Graveyard simply will not/ cannot be destroyed.
No, Power Tool Dragon has no such negation effect.