Yeah, the duplicating quest is a known issue, I was an idiot that forgot to add a quest stage check for that to the event that starts it.
The demo's pretty small though, it's only the first main quest and the first star system (plus all quests in there, which is around two or three). Same with the door, in the final version taxis are gonna be a feature on most major homeworlds, for now the door's there as a placeholder.