No question about it. She is providing false documentation to deceive the landlord about her son's qualifications for the apartment. That's fraud.
You might. If you had no involvement in this other than she used your address then you aren't guilty of the fraud. The question is whether the police and prosecutor would believe that you did not have some active role in all this.
Might want to consider whether you want to stay in a relationship with a woman who apparently has no qualms about deceiving others to get what she wants. That could end up biting you some day.

