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.
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Bottomless Trap Hole does not target, so Tyrant Dragon is unable to negate it.
No, she can only negate Spell, Trap or Monster effects that Target. Dark Hole does not target anything.
Bottomless Trap Hole can be used against a Synchro Summoned monster with appropriate attack, but it's not accurate to say it 'stops' the summon. In game terms, the summon is completed successfully, and cards like Bottomless Trap Hole will be used in response to that successful summon. It means though that Synchro Monsters like Brionac may have already used their effects due to player Priority - if you want to avoid even that happening, you need to negate the summon instead, with a summon negation card.
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 depends on the circumstances. Generally, "Bottomless Trap Hole" will be the better card; it works on Special Summons and it removes the monster it destroys from play. However, "Trap Hole" has one advantage: the monster summoned only needs 1000 ATK to trigger it, whereas "Bottomless Trap Hole" requires at least 1500 ATK. So, it would depend upon the type of deck you planned to use or went up against, but most people would choose "Bottomless Trap Hole".