Thanks for the questions!
Resilience hitting exactly 0 is an unusual occurrence and therefore triggers a rare event (an Omen). Having a full inventory does not trigger an Omen, no.
Souls are very useful and potentially game-breaking, yes. They're the equivalent of a level up and would normally only drop from the boss of a dungeon or as a special reward. Because Souls have the potential to change gameplay quite a bit I've left it mainly up to interpretation by the warden (GM).
Runecairn is primarily designed to be a game for one warden and one player (so no typical adventuring parties), mainly for reasons you mention (the bonfire breaks a lot of standard RPG convention). You can always have one primary player and have the others be summoned NPCs (like in Dark Souls) who disappear when the "host" dies.
As always, different interpretations will exist on different tables and with different wardens, so go with whatever works best for your group!
Thanks and enjoy!
Colin