Possible. If you have an underlying spine issue, it could cause the nerves going to the knee muscles to malfunction which can cause the knee to hurt or even muscles around the knee to misfire resulting in knee pain as well. I would however still make sure your knee isn't the problem as well. Both need to be treated in order for this to work in the long term.
Both are possible. It is not uncommon for a nerve condition of the lumbar spine or a hip condition to refer pain to the knee. It is also possible to develop knee conditions (bursitis/tendonitis) as a result of an altered gate caused by "sciatica". An evaluation including a thorough history and appropriate physical exam is necessary to determine the cause of knee pain.