marinca, FAFSA does not ask for anything, nor does it give any aid. The purpose of the FAFSA is to collect information that is used to calculate the Expected Family Contribution as outline by Congress in the federal methodology. Individual schools verify your information from documents they request.
As for your situation ... if you are filing as separated, you can complete your tax return either way. The thing is, though, that you cannot live on $1000 a year. How do you live? Who pays for your rent, food, car expenses, etc? If the child support you claim is a large number, that may help explain. If you receive federal benefits (food, housing, etc), that will be explained when you check the federal benefits box. If you are verified, you will have forms to complete that will explain all of that.