2.3 - If my PC died at the end of Dragon Age: Origins how are they alive in Dragon Age: Origins - Awakening?
If a player wants to, they can import their "Dead Warden" into Awakening and play as them. For the story it's assumed that they didn't make the ultimate sacrifice, instead somehow survived. A player would start as the same level with the same gear as their "Dead Warden". Essentially, if a player doesn't have a problem hand-waiving the story in this regard - neither do we.
2.5 - Will my items, armor, stats, etc transfer over if I import my character from Dragon Age: Origins?
Almost all items are imported with your character. The only exceptions are the Origins promotional items and DLC loot, which were meant for Origins alone.