Your custodial parent is your father because you live with him. It’s his income that goes on FAFSA. Money that can be attributable as “gifts” to him are not considered income. Anything that you can attribute as going to him as a gift that is then used to run the household should not be reported as income. If your mother clearly has it recorded and indicated that the $10k she gave your father in 2018 was child support, then it has to be listed as such. If it’s just a gift to him or shows as such, then that’s a gift.
Income for FAFSA purposes and financial aid are totally different things. However, monetary gifts to your father are treated pretty much the same; he is not supposed to report monetary gifts to The IRS as it does not charge taxes on monetary gifts, and FAFSA does not expect a parent to report monetary gifts either as untaxed income.
You do not report assets on the FAFSA unless the money is actually In your account or in hand the actual date you submit the FAFSA. In fact, it’s advisable to pick the date you press the send button to be a day AFTER expenses have been paid for the month and not the day you are sitting flush in assets with payables. A check in the mail may not arrive for any number of reasons.
YOU, the student, are supposed to report as untaxed income, any money you are given in gifts, tips, as well as any bills paid on your behalf by anyone other than your father. It’s called untaxed income because most of the time you will not owe taxes on it, it doesn’t show up on your tax return. As said earlier, income to the IRS and FAFSA do not necessarily jive. You do not have to report gift money to the IRS any more than your father does. However, FAFSA requests this information. Any money given directly to you or on your behalf is supposed to be reported as untaxed income to you. If your non custodial parent (mother) gave your custodial parent(father) money for you, that is considered child support or untaxed income to you. It can come down to how that money is reported.
On a pragmatic basis, most kids do not report small gifts, even money on FAFSA. Actually, $5 given to you for walking the dog or as a gift, it does not matter, is supposed to be reported on FAFSA as student income. But as a matter of practice, most kids do not even track small gift amounts of cash. I doubt birthday, graduation, holiday gifts are reported as untaxed income to them by students on FAFSA as technically they are supposed to be. It’s a gray area that is not pursued, though if there is a paper trail that is there if you are selected for verification of this sort and scrutinized, and you deposited money into your bank account, for example, it is possible it can come up.
The $10k in medical bills paid on your behalf by someone is an issue. That is supposed to be reported on FAFSA—not to IRS, they do not care about monetary gifts, or “on behalf” payments of this sort. FAFSA does ask for this and that could be a very heavy hit in your EFC, as half of any amount you receive as income over $6660 is added to your EFC.
Note that the parents’ untaxed income section does not include a question for “money received, or paid on your behalf” while the student’s untaxed income section does.