He will appear before a Judge and the charges (the reason the government thinks he should be deported) will be read and if necessary explained to him. The first court date has most likely simply been dismissed in favor of the second one. Assuming you are a US citizen - or a resident, for that matter - you can petition for Luis. You should, however, meet with an attorney to discuss whether Luis is even eligible to stay in the US (and ultimately get a green card).
There are many factors involved here that really cannot be answered in a forum such as this, such as whether or not you are a US citizen, whether your boyfriend is still in the US and whether he has ever left. In general, if he has remained in the US, he will not need a waiver for the overstay, assuming you are a US citizen, but there may be other issues. You should consult with an attorney to review your entire situation.
There is no single answer to this question as every case is different. Generally speaking you need to prove the bona fide nature of your marriage (real marriage and not a "Green Card marriage"), your legal entry or any exception for which you qualify, no disqualifying criminal record... I would suggest you sit down with an attorney and discuss your case in person.
Definitely you should file for a FOIA to get his records. He can use a validly issued Social Security Number for tax purposes. When you say a court hearing, are you referring to immigration court? Or do you mean an interview for his green card before USCIS? If it is immigration court, he may have an order of removal against him. Consult with an attorney before you do anything.
It is risky to leave under these circumstances. Citizenship and Immigration Services can give Advance Parole and Customs and Border Protection can still deny you entry into the US. You may also be subject to a different bar on entry if you have been in this country for a certain period of time in an unlawful status. I would not advise you to leave while your case is pending.