You can go to the biometric alone. Make sure you bring your ID and the biometric appointment letter. During the appointment, the service will take a picture of you. They will also check your fingerprint.
This has nothing to do with your "illegal" stay. The service will check your criminal history.
You may want to consult with a family law attorney in California. In many states, a person's immigration status is irrelevant therefore a person is able to obtain a court order against ex-partner to pay.
When a person enters the United States on nonimmigrant visa like B2, the person must have nonimmigrant intent. If not, like my colleague pointed out, the person commits immigration fraud. There are legal ways to do this like filing K visa or IV. Consult with an immigration attorney.