If you are entitled for 60 days visa exemption on arrival then book a dummy onward tkt showing departure from Thailand around 58 days from your entry date which might cost around $15/-.
50 days into Thailand apply for extension and by then you’ll know how to handle going forward
Don’t waste time waiting for a answer that makes you feel good BUT just go directly to the Embassy or the nearest Consulate and hear it from the horse’s mouth
Yes, legally she can apply locally in the US for a parole/absence from USCIS for up to a year and even 2 years under certain circumstances.
Remember those absent days away from the US will be deducted from the number of days the applicant must be physically and continuously be present in the US before the application for citizenship is approved.
(Continuously 30 months presence in the US before the application can move forward towards citizenship)