Or in general, just how these cards interact.

I'm new to the game and was playing at the Summons with a Crab opponent. He has reprieve on a bowed Vanguard Warrior, he sacrificed the Vanguard warrior, reprieved it back, and when it was reprieved he unbowed it. Is this correct? Is the vanguard considered to have left play and re-entered it from the sacrifice/reprieve mechanic?

As well, is sacrificing the Vanguard warrior considered to be the cost for placing a fate on a character? Meaning if I reprieved it, I would or wouldn't still get to place a fate on a character.

With Reprieve, the character never leaves play, so it stays exactly as it was (in this case, bowed). Also, sacrificing the Vanguard Warrior is the cost of its ability (it's before the dash and isn't a triggering condition, a restriction or targeting), so if it's prevented, the ability stops resolving (before being considered used).

Thanks for the clarification!