The above is true. The spousal visa process is completed by an interview and issuance of the visa in your home country.
You can start the spousal visa process from anywhere in the world. Your husband starts the process after marriage.
You can enter the US via the F-1 for the purpose it was issued- To attend school.
You don't need a visa to exit the US.
You can enter and exit the US during the spousal visa process if you have a valid visa, and at the discretion of CPB. You must enter for the purpose the visa was issued.