Yes. As part of your marriage based green card application you will also apply for an advance parole document (on Form I-131) which will allow you to return after temporary foreign travel. It is part of the I-485 package and the fee is included with the I-485. You should get it within 2-3 months after receipt of the I-131 by USCIS.
You will be eligible to apply for citizenship within 2 years and 9 months from the validity date on your green card, provided you still stay married and are living in the same household with your ISC wife through whom you got your GC (no other, even if USC) OR:
4 years and 9 months after GC validity date if no longer married to that USC current wife of yours.
! Don't forget to file your I-751 on time, prior to filing for your citizenship!
Absolutely you can. Parents of USCs, as long as lawfully admitted into the US do NOT get penalized for having fallen out of status or for having accumulated "unlawful presence."
You can file an I-130 and an I-864 Affidavit of Support on her behalf right now (as long as she's been in the country for at least 60 days or more, which based on your facts she has). At the same time mom will file the Form I-485 Adjustment of Status (AOS) package forms (G-325, I-765; I-131), as well as undergo...
Absolutely. Immigration laws being federal, any lawyer licensed to practice in any one of the 50 states can represent you with USCIS and Immigration court, not to mention all federal courts. To give you a realistic example, here in Southern California we have quite a few lawyers practicing immigration that are not members of the CA bar (the toughest bar exam in the nation, closely followed by NY) but in Arizona, Idaho, just to name a few.
Hurry up and hire him the best immigration lawyer money can buy, to go in visit him into the ICE detention center where he is headed next, examine his case tombe able to plead any forms of relief he might have. He may be able to bail him out, and plan his deportation defense strategy.