Are these cracks small enough to paint as gap fill or do I need to caulk?
In these cases, the cracks occurred due to seasonal moisture changes or structural movement. I'd be pushing some latex painters caulk into each crack as deeply as reasonably possible. This will reduce both the chance and the effect of recurrence. 

Cut the tip of the tube as small as possible and at roughly a 30 degree angle. Press the opening snugly against the crack as you move along the joint. Wipe any squeeze-out away with a finger or cloth. In the case of the crown molding, try to leave virtually no cove in the caulk. It should fill the crack without changing the shape of the assembly.

You can paint within a few minutes. The caulk will skin over rapidly, and since the cracks are very small there shouldn't be much shrinkage.