yes You can
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Bottomless Trap Hole does not target, so Tyrant Dragon is unable to negate it.
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".
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.
You can't use Bottomless Trap Hole in the Damage Step of the Battle Phase (the period of play that starts when the defending monster is flipped, to the time monsters destroyed by battle go to the graveyard and anything that triggers from that finishes resolving). But you can't use Call of the Haunted during those times either, so any valid use of Call of the Haunted can have Bottomless Trap Hole used against it if the monster has enough ATK. If Gorz is being summoned outside the Damage Step, then yes, Bottomless Trap Hole can be used against him. If he is being summoned due to battle damage, this is in the Damage Step, so Bottomless Trap Hole can't be used against him.
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.