Can I get U visa status even if the abuser is undocumented? What if we are not married?
Yes. The immigration status of the abuser does not matter for U visa status (unlike protections offered under VAWA). The abuser can be undocumented, or s/he can be a U.S. citizen or lawful permanent resident. Also, unlike VAWA, you do not have to be married to the abuser to be eligible for U visa status.1 If you were abused by an intimate partner, the only thing that matters is that you meet the qualifications for getting U visa status as explained in the Eligibility section.
1 INA § 101(a)(15)(U)