I will apply through my husband whose position agreed to sponsor him for a green card. We are both PhDs
Just to clarify - you have maintained F-1 status since your entry at the age of 14, are married to another foreign national, and your spouse would be getting a green card based upon employment (you would be a derivative beneficiary as his spouse under the employment-based case - he isn't sponsoring you for a family case as his spouse), right?
The big question I have is how long you worked without authorization. Up to a certain amount of time, it may be forgiven. If longer than that time, it can be a problem - though perhaps not a fatal one (would just require that you process abroad, causing some delay and inconvenience).
Speak with an attorney about this.
If he is a US citizen, then yes.
You should retain an experienced immigration lawyer to review all the facts and advise you accordingly.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.
Your issue is not whether you worked or not (as marriage to U.S. citizen "cures" that defect pursuant to INA 245(c)) but whether or not you marked your I-9 at the waitress site and indicated you were a U.S. citizen. That would constitute a permanent bar to permanent resident status. Although not heavily weighted against you in the exercise of discretion, the adjudicating officer can ask you questions about the employment, can investigate that employment and can make your life a bit miserable. [Especially since you are filing in the Cleveland District. There are a couple of AO's who would love to make your life rotten.] Hire a lawyer for the process.