Legal Question in Immigration Law in California

He can only remain in the U.S. legally if he can qualify for another non-immigrant visa status, There are too many to list here, but, in most cases, he would need an employer-sponsor & meet the other visa requirements. If he wants to study here, he will have to return home to apply for the F-1 visa abroad. USCIS does not like to give changes of status from B-2 to F-1.

He cannot get a "work permit" any time soon, unless he qualifies for an H-1B visa, which is too complicated to get into in this forum. You can find more information at www.uscis.gov & search for "H-1B".

If you get married now, he cannot immediately apply for a "greencard". I suggest waiting until you become a U.S. citizen. However, if he remains in the U.S. beyond the duration of his B-2 admission, he risks the possibility of Removal if he is caught without legal status, especially if he works without authorization.