The 843 would be filed separately, it's not part of your regular tax return. There's no specific deadline, although you should probably file as soon as you get written confirmation from your employer that they will not refund the SS and Medicare tax they adjusted.
https://www.irs.gov/forms-pubs/about-form-843
You'll need to file the 843 by mail since it's a separate claim and not available for e-file, you can still e-file your regular tax return as usual.
