luymel

2 - 3 weeks
https://www.avvo.com/legal-answers/if-the-lock-box-rejects-my-i-485-package--for-any--2174511.html
What mistake did you make? They might send you RFE for it instead of fully returning it.

Thankfully my dad co sponsored my wife
 

1. Regarding the fee issue. USCIS will reject you and return your whole package to you. I know this because I put down the wrong amount of fees on my check, and they rejected it and sent it back. The whole package will be returned so no need for extra paperwork. You need to pay for the fees. If this fee is too much for you, did you have a co-sponsor for your petition?
2. If she already overstayed her visit, she can't leave until she gets her AP. When I applied in 2014, it took me 5 months to receive my AP.... the day AFTER I got my green card. I don't know why, maybe I was just that "lucky".
    I was in desperate need to return to my home country to visit my father since he was diagnosed with cancer and had to go through a series of treatments. I successful applied for an emergency AP but I don't know if your case counts as emergency.

Agreed. As you now know, there is no fee waiver for a normal I-485. You must pay the entire fee yourself. 
 
Wait for the application to be rejected by USCIS and returned to you, then pay the fee and re-submit.