Is there any side effect from using mouthwash regularly? Is there any product available which can remove the firm black deposit (tartar) frm teeth?

Regularly, no; Although anything can be taken to excess, regular mouthwash use is safe. Resistant tartar is best removed by dentists during routine twice-a-year checkups, and they can also tell you how to best avoid the build-up in the future.
Dental Hygeine 101. Flossing daily and using a "waterpik" type device can also help. Try a new type of electric or manual toothbrush; change them every three months. Check with your dentist to make sure you're brushing your teeth correctly and massaging your gums. Clean your tongue to curb bad breath, too.
Not really. I would use an alcohol free mouthwash especially, if you use mouthwash on a regular basis. You must see you dentist at least every 6 months to have the calculus (tartar) removed from your teeth.