Since you are in the US on F1 visa status, you should not consular process. Rather, it is better if you do a one step adjustment of status application in the US. In that case, you would submit the I-130, I-485, I-765 (application for work permit, I-131 (Application for advance parole to travel), and all other accompanying documents. It takes about 3 months for you to get your EAD after filing all these docs. Consult with an immigration attorney to guide you through the process.
You cannot legally work in between current ead and new one getting approved. However, if you do work without a current balid EAD, your unauthorized employment will not bar you from adjusting status because your wife is a US citizen.
You are only able to lawfully work with a currently valid EAD. There is no conditional work permit, but when you apply for AOS you can apply for a work permit, as well, which will take a few months or so to process. You really should work with an immigration attorney as it appears you are in dire need of some rather basic immigration advice.
Gunda J. Brost Brost Law Office This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.