The answer depends on the timing of your N-400 and your level of comfort in having your family here without authorization. If you've already filed for naturalization and you're in the Boston area, chances are you will be called in for an interview fairly soon (if you haven't been already). It WILL be possible to adjust their status even if they're no longer in status by the time you naturalize (and any period of unlawful presence will be forgiven, provided they don't leave the U.S. before you...
Again, there are different kinds of "dismissal". If your dismissal involved some admission of guilt on your part, this may be considered a conviction for immigration purposes. Take your criminal docket sheet from that case and bring it to an experienced immigration attorney for advice.
Gregory Romanovsky, Esq.
12 Marshall Street
Boston, MA 02108
If you fail to convince USCIS that the marriage is legitimate, USCIS will deny the U.S. citizen's I-130 petition on your behalf. The immigration judge has no jurisdiction over the I-130 petition - you will have to appeal the initial denial to the Board of Immigration Appeals or file a new I-130. But if you are already divorced by that time, you are, most likely, out of luck.
Gregory Romanovsky, Esq.
This year, they hold him 4-5 times each month. There is no public calendar available that you can view, but you can certainly request to speak with a supervisor upon the conclusion of your interview, to alert them of your travel plans and request your oath to be scheduled outside of those dates.
If she is a U.S. citizen, she can travel with a U.S. passport that you will need to obtain for her and a signed permission from you, as her parents (without it, they may suspect that the baby is being stolen).
If he had entered U.S. legally and then overstayed, he may be eligible to get his green card without leaving the U.S. (assuming there are no other grounds of inadmissibility, such as criminal record, fraud, previous immigration violations, etc). If he had entered without inspection, he would have to leave the country and re-enter with a waiver. The prospects of getting that waiver depend on whether you can show extreme hardship, which, in turn, depends on many factors. Talk to an immigration...
Most likely. I suggest that you schedule a consultation with an experienced immigration attorney and bring copies of your entire file. The attorney would need to look at the history of your case to provide you with specific advice.