If another creature enters the battlefield as a copy of the Bat token or another effect creates a copy of the Bat token, it will not have the triggered ability granted by Timothar.

If the exiled card is somehow no longer in exile when the Bat token's triggered ability resolves, you will still sacrifice the Bat token.

Timothar's last ability is linked to the ability it grants the Bat token. If a replacement effect causes you to create more than one Bat token with this effect, they will all have that linked ability, and the exiled card will be returned to the battlefield if any of them deals combat damage to a player.

The controller of the Bat token as it deals combat damage to a player will be the controller of its triggered ability, and the exiled card will be returned to the battlefield under that player's control.

The ability of each Bat token you create refers only to the card you exile during the resolution of the ability that created that token. When it deals combat damage to a player, you return only that card to the battlefield, not any other card exiled by Timothar.

Timothar's last ability triggers when any nontoken Vampire you control dies, not just nontoken Vampires you own. If you control Timothar and another player's nontoken Vampire and that Vampire dies, you may pay {1} to exile that card from their graveyard.

If you can't exile the card, perhaps because another effect moved the card before the triggered ability started resolving, you can't pay {1} and won't create a token.