An I-601 is the form used to apply for a waiver of a ground of inadmissibility. You do not say what inadmissibility the consulate is applying to her case. You need to consult with an attorney about waivers, including possibly a fraud waiver. Good luck!
I do not exactly agree that you should just file an application for adjustment of status. I agree with my collegue that you need to seek immigration counsel from an immigration attorney. The attorney will need to review the legality of your prior entry, whether your spouse is active military and whether you might qualify for parole-in-place which might qualify you for adjustment of status depending on many other complex factors. If you file an application and do NOT qualify for residency, you...
I agree with collegue: you need to bring all the conviction documents to an immigration attorney who is experienced with immigration consequences of criminal convictions. Your boyfrined might be an "aggravated felon" (lawyer must review case) and barred from coming back to the U.S. for a LONG time. If an aggravated felon is caught re-entering, the prison sentences arte up to 20 years.
ICE tiene 48 horas lunes-viernes a pasar por ud. Si no pasan, ud. puede demandar el sheriff o warden con una habeas corpus. PERO si pasan y ud. tiene un record de drogas o un delicto mayor (felonia) ud. NO tiene el derecho para una fianza de custodia del ICE... Hay que consultar un abogado de inmigracion si los cargos son seriosa o si ud. quiere saber sus derechos...
I agree that first you need to protect yourself. Then seek professional advice about whether or not you can file under VAWA or otherwise. I would seek a lawyer with significant immigration experience who is also a member of AILA.
An immigration attorney should review the facts of the removal case, family connections, immigration and consular waiver options (if any). An attorney might also consider a motion to re-open removal proceedings and the possibility of parole back to the U.SD. depending on ICE's position... There is no way to answer your question without a lot of time spent studying these facts you have described.
He should consult with an attorney who handles removal defense. He might qualify for cancellation of Removal or other releif as well as for an immigration bond. If so, he might be able to apply for work authorization, social secuity and a driver's license 9=(depending on state law where you live). A deportation lawyer will need to review his immigration, family and criminal history to accurately advise him.