USCIS memoranda indicates that a DUI is a "significant misdemeanor" that would prevent approval of a DACA application. Also, expungements generally have no effect on the immigration consequences of a conviction. In any event, you should consult with a qualified immigration specialist to discuss your all of your options, including DACA.
Immigration Judges maintain the record of proceedings in the EOIR. the "A File" is the alien's file with the DHS. Many documents from the A file may be filed into the ROP, depending on the purpose. The rules of evidence are more relaxed in immigration proceedings than in judicial court proceedings, which can be both good and bad for a respondent. Consult with an immigration attorney for advice and/or representation in court.
It sounds like you have filed an I-751 petition, but it is not clear if you filed it jointly with your soon-to-be ex-wife, or are seeking a waiver of the joint filing requirement. You cannot seek a good faith waiver unless the divorce is final. I recommend that you consult with a qualified US immigration attorney immediatey to better understand this process.
It sounds like he will be referred to USICE for removal proceedings. Consult with an immigration attorney to determine whether he has a chance for release on bond from USICE and any defense to removal proceedings.
Generally, a DUI will not implicate one's good moral character, but "special circumstances" may alter the analysis, especially if you are incarcerated during the statutory period. I recommend that you hire an immigration attorney to work with your criminal defense attorney in arriving at the least damaging plea agreement.
Simple DUI's are not necessarily "crimes involving moral turpitude," which can be deportable offenses, however, multiple and/or aggravated DUI's can rise to the level of a CIMT. Please consult with an immigration attorney as soon as possible to discuss your husband's case.