Nyc - My Father Owes 60k In Back Child Support Because My Mother Committed Welfare Fraud.

NYC. My parents separated in 2004. My father left the family home and became essentially homeless for some time. I stayed with my mother until 2005, when she had a mental health breakdown and I moved in with my grandparents. During this breakdown, as she was no longer able to work, a social worker at the psych hospital she was in assisted her with applying for welfare / other benefits. Even though I had not been living with her for a couple of months at this point and there was no plan in place for me to return, she stated that I was living with her on her application. She apparently claims that this was in good faith as she thought I'd be coming home soon. When she began receiving welfare, a child support order was opened against my father - which I know is standard and makes total sense, except a) I wasn't living with her for her to support and b) my father was homeless and ALSO too sick to work.

My mother received welfare benefits for both her and me from approximately mid 2005 - late 2008, until she qualified for SSDI. During that time, I only returned to live with her for about 4 months, but her home was not my legal address. There are court orders, medical records, and school transcripts proving that either my grandparents or my aunt had custody of me during those years. While my mother received those benefits, my father racked up over $60k in back child support. He did not have the money, means, or mental health to fight this at the time, or any time since.

My father has of course had his drivers license and professional license suspended due to the back child support, so even if he became well enough to work (which is not going to happen now) he couldn't. He should have applied for SSDI himself years ago, but to my understanding any lump sum he is awarded will go straight to the child support arrears. He lives a very difficult life while my mother got away with welfare fraud.

My questions:

1) This was obviously a long time ago! Google says the statute of limitations on welfare fraud is 5 years "from the date of discovery". What exactly does that mean? Is it too late to make a report?

2) Let's say that I report her, and there is an investigation, and it's successful (a lot of ifs!) Would it then be possible for the child support my father owes to be removed? I imagine he would still owe something to somebody, but not to my mother, and not in the amount of $60k.

3) If there's a statute of limitations on welfare fraud, would the records that I was not living with my mother help in reducing / removing the child support arrears on their own?

I know we are likely out of luck here. But thank you in advance for any input!