1) Does this event have to be completed by JUST Characters, or does the card text mean that, ON TOP of your basic ship stats, you can only use characters, and not things like Photon Torpedos, Fire all Weapons, etc.?
Ship stats are not counted either. You need the stats from characters only.
2) And, however it works out, is it supposed to be a thing where everyone playing can COMBINE their stats.
Yes, all players combine their stats.