I have sciatica, but usually it only goes down to my knee. I guess it is possible that if it is bad enough of a case, you could feel it down past your knee. If you are feeling pain in the soles of your feet, I would put it to something else first though, rather than back pain. Sciatica definitely does not cause pain in your hands.

Do you think you might have a circulatory problem?

I found that walking actually worsens my sciatica. I think it depends on the reason why you have it whether walking is going to do good or not.