I think the issue of FICA taxes on an F-1 visa is separate from the residency issue.
I agree that, having chosen to treat your spouse as a US resident for tax purposes, that is permanent unless you can get the IRS' permission to revoke it. Exactly how you would do that is unclear. It might be that you just file separate returns and include a written statement requesting to revoke your previous election, and see if the tax returns go through. Or, it might be a more complicated process. If you really want to revoke the election, you should get professional guidance. However, being treated as a resident is not what triggered FICA withholding. (The employer probably doesn't even know what you did on your tax return.)
On the FICA issue, F-1 students are exempt from FICA as long as their work is connected with their education. If they work outside of their educational program, they are subject to FICA whether or not they are being treated as residents. (In other words, residency is not directly connected to FICA, but rather, it is about the nature of the job and the relationship of the employer to the school.)
This is the same with students who are US residents--they are exempt from FICA if they work for their school as part of their degree program.
This then goes to internships -- if an internship is arranged by the school and is a mandatory part of the degree program, it should usually be exempt from FICA both for US citizens and for F visa holders, but if the job is not arranged by the school and is not directly related to their degree program, it is probably correctly subject to FICA, both for US citizens and for F visa holders.
There is a form 843 that can be used to request a refund of miscellaneous taxes including FICA and Medicare tax. You would have to very clearly describe the circumstances and include proof that the job was an official part of the student's education and should have been exempt from FICA and Medicare withholding. I can't guess your chances of success.
@Hal_Al do you have any further comment or clarification?
