Background check completion varies for people. Some clear it within a day, others could take weeks/months. Once the biometrics gets captured, they initiate a FBI background check. Depending on what the initial check turns up, they may need to escalate and conduct some additional checks.
GC background check is a lot more extensive than that conducted for the VISA. USCIS will not waive the background check based on what was done at the embassy level for your VISA approval.
Yeah, the F-1 visa check was pretty annoying to me because I did laser physics for my foreign master's degree. Then, I came to US to do PhD. Worst decision ever to pick this field as a profession. I think they are checking me again for the DV...