1. She's gonna have to change her biometrics.  Remember they took your fingerprints in the embassy and the port of entry. Don't think you can get away with that , unless you alter your fingerprints.

2.  If she changes her passport, then she has to change her name too....but as soon as the name is put on the database by immigration; its gonna pop up. And don't think that USCIS can't find your departure record even if you don't submit your I94 on your departure. There is a law called Patriot act, under which USCIS, Department of Homeland security, and TSA share a common database that tracks the booking and purchasing  and boarding of an airline/airline tickets. It is just couple of Kb's of data they need to. 

3. How can a out of status person can marry a permanent resident to get back on status. 

(to change status one has to be in some sort of valid status which she don't at this point of time)

Just my couple of cents. BTW I go to law school!