1)When the non ring bearer (player A) arrives at the last space, and survive the roll..does it mean the ring will be placed on mount doom?
I think that's the right way, though can't honestly recall the last time I've had to roll for the final space, I use the Ring to land on it (or past it) and thus don't have to roll there.
after that does player A roll the threat dice again or the next player (b)(in order to destroy the ring)?
Yes, player A is the active player, so he will roll.
2) when player A (non-ring bearer) reached the last space at mount doom but fail to survive the die roll, is the ing still place on mount doom for player B to destroy...or the game ends right there?
Player B would become the active player and roll.
Chris Lawson has an excellent FAQ page for LotR: