Finality counters aren't keyword counters, and a finality counter doesn't give any abilities to the permanent it's on. If that permanent loses its abilities and then would go to a graveyard, it will still be exiled instead.

Finality counters don't stop permanents from going to zones other than the graveyard from the battlefield. For example, if a permanent with a finality counter on it would be put into its owner's hand from the battlefield, it does so normally.

Finality counters work on any permanent, not only creatures. If a permanent with a finality counter on it would be put into a graveyard from the battlefield, exile it instead.

If you somehow activate The Tome of Aclazotz's ability more than once during a turn, you can cast a creature spell for each ability's permission. Similarly, if another effect allows you to cast a creature spell from your graveyard, you may use that permission and later use The Tomb of Aclazotz's ability to cast another creature spell.

Multiple finality counters on a single permanent are redundant.

The creature spell you cast will be a Vampire in addition to its other types while on the stack. The resulting creature will be a Vampire in addition to its other types.

You can discard your hand even if you hand has zero cards in it.

You don't choose which creature spell you're casting while activating or resolving The Tomb of Aclazotz's last ability. The ability creates a permission for you to cast a creature spell from your graveyard later in the turn.

You must still follow any timing restrictions and permissions for creature spells you cast with the permission granted by The Tomb of Aclazotz's last ability. Normally, you'll be able to cast them only during your main phase while the stack is empty.