May I cast Grave Birthing, Cremate or Purify the Grave in response to the opponent targeting an instant or sorcery with converted mana cost 3 or less from the graveyard spell with Goblin Dark-Dwellers in order to exile it (so the opponent can't cast it and he can't choose another spell in graveyard)?
Yes, since the spell is chosen (targeted) when GDD's ability is on the stack, and it will only be cast at the resolution of the ability, you can respond by removing the targeted spell from the graveyard.
Note that with Grave Birthing if they have more than just the targeted instant/sorcery in their graveyard they can exile that and still be able to cast what they want.
The other two spells you mentioned target a card in a graveyard, so they'll work just fine.
However you should know, that Grave Birthing doesn't exile a card of your choice, but one of your opponents. So the scenario you described only works if the Goblins target the only card in the graveyard.