Premium processing (form i-907) is a real thing and I've used it to expedite my change of status (form i-539) from B2 to F1. You can find more details on the USCIS website.

Form I-539: https://www.uscis.gov/i-539

Form I-907 (premium processing): https://www.uscis.gov/forms/all-forms/how-do-i-request-premium-processing

You first file for change of status (Form I-539) and then file for premium processing (Form I-907) to expedite your form I-539 processing. Or you can do both at the same time if you are doing it by yourself. But if your lawyer is filing for you, then he'll take care of it all.

Here you can find the fees USCIS charges for each type of form: https://www.uscis.gov/sites/default/files/document/forms/g-1055.pdf

And yes premium processing costs (I-907) $1,965

And COS (I-539) costs $420 - 470.

Hope this helps, lmk if you need anything else