Im looking to build on a moon which is owned by nobody, but the sector and system is owned by faction, do I need to request permission to build on the moon?
You don't need permission to build a city on an uncontrolled planet.
You do of course still need permission from the city owner to build something in a city, even if the planet itself is uncontrolled.
a) If you already own a city there: no
b) If there are free squares for a city, you can place one with out needing any permissions, after that goto a)
c) If you don't own a city there, you will have to request permission from the city owner.