If I gift money I received AFTER filling for FAFSA, do I have to report it to my school or FAFSA?

20% of your assets will be added to your EFC (assuming no special circumstances like your parents qualifying for auto-0 EFC). So 20k = 4k higher EFC.

FAFSA does not give money. It is just a form to determine whether or not you’re eligible for federal aid. Pell eligibility (grants for low income students) drops off around an EFC of ~5300. Your 4k in assets already puts you very close to that limit.

Everyone who files a fafsa is eligible for Direct loans (either subsidized or unsubsidized depending on your need) and you may qualify for federal work study (again depending on need).