You cannot file the FAFSA until you have your green card because you will need your A# and social security number.
You can and will need to put your parents income and assets on the FAFSA when it is time for you to fill it out.
You will just put all 000-00-0000 in the social security field
Your father will have to use his tax ID number (if he has one) to get either an IRS transcript or non-filers form from the IRS.
You will be flagged for verification and your parents will have to provide documentation on how they meet their basic needs (food clothing and shelter)