Adjustment of Status - I-485

Please here is my timeline.

I am a U S citizen and i petitioned for my husband 2016.

We filled for i 130 and i 485 together which was received on March 1, 2016.

during this marriage i cheated on my husband which my high school pregnant which result in pregnancy, and my husband didn't want me to abort it so we keep the baby.

We had our interviews as follows;

November 8, 2016 at Newark NJ field office. No approval because we mismatched a lot of questions
We were called for 2nd interview on January 2017 which was stoke interview. We were interview for several hours and scrutinized. After the interview, we didn't hear any response until last Friday.

On May 16th, a NOID was sent to our old address of 3 years with no update online. The guy who still lives there was nice by given us the letter.

The problem on the letter was stated as follows:

USCIS records indicate the following:
I claimed single on a public housing record on September 2016
You applied for housing assistance on September 2016 with the beneficiary not listed as resident.
You have the same address on your drivers licence
Me and my baby father registered a baby shower together in which we never honored.

The problem now is that they want me to rebuff the claimed withing 30 days which is already 12 days today.

I need help on NOID response please and what are his chances of getting his 10 years green card because we have been married since 2015 and we have documents together with our house different from the housing assistance they accused me of. My mother was the one who applied for the Housing assistance and i and my son was listed as a residence by my mother.