1. Where you respawn depends on if you're on a mission or just out exploring doing a quest. If your whole party dies during a mission, you respawn back at the outpost. If your whole party dies during a quest, then you respawn at the ressurection shrines. You will however have a death penalty. IF you die, but your companions kill all the monsters, then they can ressurect you (if your party has a monk, or if some of the players carry their rezz signets)
2. You don't lose your items.
3. There is a vault in every outpost. This is account based, so all your characters can access whatever you'lve put in there. Makes it very handy to 'give' your new character something your higher character has found.
Hope the answers helped.