A: Whether your children are entitled to request U.S. passports depends on various factors.
Unfortunately, you provided limited information in your posting.
Are you a U.S. citizen since birth or are you naturalized?
If naturalized, when did you become a U.S. citizen?
Are your children U.S. residents?
The above information is required to provide you with meaningful guidance.
A: In your posting, you did not indicate how and when you obtained your resident status.
Without knowing that information, it is probable that you may have to file the FORM I-130 on behalf of your ( unmarried ) child.
You should contact an experienced immigration attorney for personalized guidance.
A: As a permanent resident, your mother will need to file a relative petition on behalf of her spouse.
An experienced immigration attorney can provide you with personalized guidance to avoid delays with this case matter.