There is no immigration law against using one's social security number on an application for a lease.

There is no limit to how many times CIS can extend the prima facie notice.

You can do that. And you could also get married now and have her apply for an H4 and enter on it now.

Contact the ombudsman's office. Get instructions what to do. Perhaps they will let you file it again now.

EB3 is the category for which she may qualify.

If you depart the US you will have a problem. If you have proof you currently have DACA you should not have a problem.

it means USCIS has not yet approved your I-485.

They will certainly consider it, but it should not completely preclude you from naturalization.

One does not have to pay a fee for an I-131 based on a pending i-485. Not for the first I-131, nor for the renewals.

It does not appear to me that you have accumulated any unlawful presence.