I live in Georgia and I have a F-1 visa.

I got 1099 MISC form a month ago . Box number 7 is filled only.

My question is that

1)Should I fill out Form 8843? What is the advantage of filling this form?

2) Also, Should I fill out State 500 form? What is the advantage of filling this form?

For federal, you must file nonresident tax return and Form 8843. Also for 1099-misc income complete schedule C or C-EZ.

1099-misc. You must file your tax return if your income is $400 or more. You will report your income and business related expenses on schedule C or C-EZ (Form 1040). Then you put net income (or loss) on line 12 of Form 1040. This income is not subject to SE tax (SS tax and Medicare tax). You must pay income taxes.
Even though schedule C treats you as a self employed, which may not be correct for you, this is how you must report this income. Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents (http://taxipay.blogspot.com/2008/03/us-tax-filing-requirements-for-non.html)