The Nexus - when does its ability resolve?
I'm unclear about the timing of the replacement. Does this ability resolve before or after the base scores? 


The ability doesn't cause the base to replaced. It simply changes how it is replaced.

Bases are replaced at the end of the base scoring process. A base is normally discarded and replaced by one from the face-down base pile. Nexus is instead replaced by one from the discard pile if possible.

This happens after points are assigned.


  If it's after, why isn't this ability worded similar to The Mothership and other bases in the base set


Space on the card? Better wording?


  Also, what happens if there are no bases in the base discard pile, does the base get replaced from the base draw pile as usual?


Yes. If Nexus isn't capable of changing what normally happens, then it doesn't.