Does sciatic nerve pain typically go down the outside of the calf muscle and back of calf?

Yes and Yes. Sciatica is the symptom of leg pain caused by a disc herniation or narrowing where the nerve exits the spine. A disc herniation is a outpouching of the disc from its normal place into the spinal canal or on the nerve and can be a source of pain in the back or down the leg or even the groin area. The nerve then goes to the muscle which can then hurt, spasm or feel sore or irritated.
L5 or S1 nerve root. L5 goes to outside of leg and top of foot s1 goes to backof calf and outside bottom of foot both are called siatica these nerve roots are major components of the siatic nerve above the knee they feel the same.