And I will explain why nomads have no reputation modifiers. And cannot have ones. If you kill nomads and your rep with another faction increases, you may kill that other faction and your rep with nomads will increase. Needless to say how unbalancing that would be: as far as I know, nomads are quite dangerous as they are now - not for capital ships, but for traders and fighters surely. If you make them neutral, trading and simply moving around in Omicrons would become far too easy.
Lost Battlestar now belongs to 'Administrator Faction', not Nomads. Nomad reputation won't influence it in any way. And this is why DarkOddity was able to dock to this station on certain stage of beta testing. I accidentally made admin faction friends of bounty hunters. This glitch was already removed, so everyone who will be able to dock to Lost Battlestar now is a cheater and should be reported.