Does piriformis syndrome cause pain at back of knee?

Yes: The piriformis syndrome is caused by the piriformis muscle compressing the sciatic nerve. Usually it causes pain and tingling in the buttocks, but if the compression is severe enough it can cause pain down the length of the sciatic nerve in the leg. There are a number of treatments available to avoid surgery. An Orthopedic surgeon or Physiatrist can recommend such modalities

Possibly: Piriformis syndrome can result in buttock as well as sciatic nerve pain. It is therefore possible to experience pain behind the knee from piriformis syndrome.

Yes: Yes. Nerve irritation or sciatica often accompany pirifirmis syndrome. Leg pain and also back pain can be present. Radiation to the back of the knee is not uncommon. Your profile indicates the presence of spinal stenosis. This, along with sciatica associated with pirifirmis syndrome, can cause knee pain. If your symptoms progress get rechecked by your doctor for treatment recommendations.

Yes: It depend upon whether is compresing the sciatic nerve or not (the piriform muscle)