If you have no other income besides social security, you would not need to file a tax return. If you did, you would have no taxable income to claim any credits and filing as Head of Household would not give you any type of refund. In order to get any type of refund of money you did not pay in, you would have to have earned income.
No, you could not claim her as a dependent if she is getting alimony of about $6,000 per year as she would be over the $4,700 threshold to claim a dependent.
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