Legal Question in Immigration Law in California

It depends what your student visa says. If your I-94 says D/S you should be ok provided your application does not exceed 6 months following the completion of your program. The sooner you apply the better it will be.

Once your OPT expires, you still have the grace period, as you are aware of. You can get married & file for adjustment of status at any time. Unlawful presence does not affect eligibility to file for adjustment of status as long as you had a legal entry & are married to a U.S. citizen. If you file for adjustment after your grace period, then you just cannot travel on advance parole while your case is pending. However, adjustment interviews are being scheduled within a few months of filing, so the inability to leave the country should not be a major issue.