Only 1/2 of limbs of Japanese mock cherry have released this year. The nude limbs seem to be alive. Should I prune them off? Most leafless limbs seem alive - but leafless. Do I cut off/prune off all leafless limbs?
Dead branches can be pruned at any time.
Any other pruning should be done when the tree is dormant, early spring or winter.
Adding a slow release fertilizer in the spring will help the tree get going. You can even use a tree fertilizer spike.
If it has been dry I would increase watering and make sure that it is a deep watering. Shallow watering does more harm than good.
Adding 2 to 3 inches of hardwood mulch will help with moisture retention.