Shall I file application right now or wait until I get citizenship?

[Jackolantern]

More details:
I've been in US for the last 10 years, and went to my country to get marry but my wife is from another country. In my country people get married in church and church sends documents to civil court and they have religious and civil documents, but in her country it's illegal to a priest to perform a religious wedding without the civil marriage first, so people get married in court 2 days before religious ceremony (right now in her country she is definitely single, but people who live together for 3 years have the same legal rights as married people in case of a "divorce").

Which country did the marriage occur, yours or hers? Is it that your country recognizes it but hers doesn't?

The US government and USCIS look at whether the marriage was legally recognized in the country where it occurred. If it happened in your country and your country recognizes it, you are married in the eyes of USCIS, and she will have to defend her claim of being single on the F1 application, perhaps by explaining that she thought she was legally single because her country does not recognize the marriage.

But if it happened in her country and her country doesn't legally recognize it, you are single in the eyes of USCIS, and you need to update the N-400 at the interview to change your status to single.