Would a pinched sciatic nerve cause pain in wrists and numbness/tingling in hands or feet?

Feet maybe, hands no: The sciatic nerve runs from the gluteal region (your rear end) down the back of your leg, then branches to innervate the back of the thigh and leg as well as the outer part of the lower leg and then parts of the feet. An injury may cause those symptoms there, as well as problems with motion. The major nerves that serve the hands are the radial, ulnar and median.

No: A pinched sciatic nerve will not cause wrist symptoms or numbness in the hands. A pinched sciatic nerve may cause symptoms of the leg.