Fong & Associates | William D. Fong
You can apply if you have 2 things (1) a basis for permanent residence; usually a USC spouse or USC adult child and (2) you are eligible to get permanent residence in the US; such as being grandfathered for 245(1) or eligible under section 245(a). It sounds like your children are minors and you are not eligible to get a green card in the US.
Answer Applies to: Texas
Eric M. Mark, Attorney at Law | Eric Mark
No. You cannot just apply. If you do, you will be placed in removal proceedings. A family member will need to sponsor you for permanent residence and you will need a waiver of your long period of being here unlawfully. You should consult with an immigration attorney.
Answer Applies to: New Jersey
Law Office of Christine Troy | Christine Troy
That depends on how you entered the US. If you entered legally, you may be able to qualify after your kids are 21 for sponsorship in the US. Unless you are eligible under 245(i) law or perhaps a U visa. Otherwise you would need to apply for the GC at your US consulate in your home country. When you leave the US, this will trigger a ten year bar to re-entering so that gets very tricky. Make an appointment with a competent immigration attorney in your area to fully go over every detail of your case.
Answer Applies to: California