she is taking her test for naturalization this month.
Cannot be determined on the facts posted. It depends on whether he is in the US in her custody and has a green card.
You should retain an experienced immigration lawyer to review all the facts, advise you, and handle the case. You can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.