But what about Intuition or Buried Alive? when you play one of those the cards/creatures will go into the graveyard first, then the Buried Alive. ( or so I've been told)
What's the diffrence between playing Intuion and Tooth an Nail for Eternal Witness?
Yes, Intuition and Buried Alive will be last to go in the graveyard when they resolve.
But, this isn't relevant at all to the situation.
The Eternal Witness trigger cannot go onto the stack in the middle of the resolution of Tooth and Nail. It has to wait until Tooth and Nail has finished resolving. The last part of Tooth and Nail's resolution is that you put it into the graveyard.
Then, the Eternal Witness trigger can go on the stack. Since the TnN is in the graveyard now, it is a legal target for the Witness trigger.
Ditto with Bribery.