In criminal cases all questions must be answered, but in civil cases they do not unless it is relevant to the case. Did she file divorce because of your criminal history? If this is the grounds for filing them yes you would have to answer it, if it wasn't then no you wouldn't. You would have to...
green cards and divorce
A divorce doesn't necassarily mean that a green card is revoked. There is a certain amout of time that people have to stay married before a person becomes a legal citizen of a country. I am not sure what the time limit is exactly but if there are marital problems no...