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.
There is no guarantee for visa issuance. You can act as financial sponsors but the bigger issue may be proving that your sister will depart the US after her temporary stay - she must show that she has substantial ties in her homeland or country of residence.
Start by filing an I130. If he is 245i eligible he may apply to adjust his status here in the US, if not he would have to consular process but may be eligible for the I601a waiver. He may also be eligible for DACA. You may want to consult with an attorney before moving forward.