The amount that you owe on the federal return is for self-employment tax. This covers the FICA tax for Social Security and Medicare.
No, you did not make a mistake on your Georgia tax return. Georgia has a standard deduction that reduces your taxable income to $0. There is a requirement to file a tax return with Georgia as long as you are required to file a Federal income tax return. Please see this for Georgia filing requirements.
And, you do not need to file a tax return with California.
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