Hardship waiver of what? If you are asking if he can get a green card because you are low income, no, generally fathering a child out of wedlock,...

She was not in status. Not sure if or why that matters but if she was not a full time student and if her OPT was denied, it is very hard to argue...

Call customer service and reschedule, very doubtful they will print you without a notice So call customer service or do it online.

No, one is not allowed to take a child out of the country without consent of both parents, but that does not mean it could not happen.

You are correct that under BIA case law, leaving with advance parole does not trigger an unlawful presence bar to adjustment of status.

Yes, you can apply for U.S. passports for derivative US citizens, even without a certificate of naturalization.

Even filing the PERM is a problem for being issued a nonimmigrant H2b visa. The approval does not change this.

Your husband is detained, has an order of deportation but that order is on appeal. Depending on the facts your husband may be able to file a...

There is not enough information to guess if CIS will approve or deny. You may consider instead just refiling the adjustment application.

No, you cannot lose your citizenship if you are a derivative U.S. citizen, by being convicted of an aggravated felony.