Does sciatica usually cause many symptoms?

Yes. Yes disc herniations can cause sciatica in more than one dermatome. If this does not resolve then consider seeing a spine/pain specialist for further evaluations.
Yes. Shooting pain down the leg is the most noticed symptom. One can also experience numbness, tingling and weakness in the leg radiculopathy / sciatica requires some type of symptom.
Few symptoms. The classical symptom of the affection of the sciatic nerve is unilateral(one sided) pain in the lower back radiating down the back and side of the leg to the foot. Straight leg raising is limited and the pain may get worse by coughing. Naturally if the disc involved does not return back to its original place one may develop complications from atrophy of the muscles involved to a foot drop.