SSI and welfare are not income for the $4300 income test; but they are support for the support test.
Her child may qualify as a dependent, if you meet the support test, but because he is not related, he cannot be a qualifying child for you, for the earned income credit, child tax credit, day care credit or Head of Household filing status.
There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. The Other dependent (qualifying relative) credit is worth (up to) $500 per dependent and is non-refundable. That is, it can only be used to reduce an actual tax liability.
