Will unconscious Outlands characters still distribute their stat modifiers to other (conscious or unconscious) Outlands characters?

yeah I believe so, those are passive effects ans aren't blocked by being unconscious. They are not ever 'triggered'

yeah I believe so, those are passive effects ans aren't blocked by being unconscious. They are not ever 'triggered'

This is correct. Ori can also draw you a card while unconscious, but unfortunately Thorin cannot gain resources because that is specifically prohibited as a part of being unconscious.