Can sciatica cause dizziness?

Possible. However the nerve that is injured that would cause dizziness is either in the head or in the brain stem. So unless these areas were injured unlikely that dizziness is associated with pinched nerve. Some people who have a lot of pain, can have a vasovagal response in which the body is trying to cope with the pain and can cause you to feel sick to your stomach, dizziness or feeling of passing out.
Not usually. Sciatic by itself may not. Sometimes the pain medications given to treat sciatica can. Some of the "nerve pills" neurontin, Lyrica (pregabalin) or Codeine can cause dizziness.
No. Sciatica specifically refers to pain radiating down the sciatic nerve, which runs down the back part of each leg and is comprised of a combination of the the lower lumbar and upper sacral nerve roots.