Should I prime just repaired areas or the entire ceiling before painting?
This is mostly a matter of opinion. You'll usually get a better (more uniform) result if you do things edge-to-edge or corner-to-corner, including primer. The undercoat can have a significant effect on the sheen (and sometimes the color) of the topcoat. 

Another consideration is lighting. If the room has few windows and low lighting, the ceiling finish will be obscure. If you have bright natural light or up-directed lighting it'll be in the spotlight, so to speak, and any variations in finish will be much more apparent. 

Since you're completely repainting, and assuming the sheen and color of the primer are similar to the topcoat, you can probably get away with just priming the repairs. Again, it's up to you as to what level of finish quality you need.