I purchased my iMac off of a private seller and the serial number reads unavailable

The iMac serial number is usually printed on the underside of the pedestal stand.

If the macOS is reporting the s/n as unavailable, I'd say there's a high probability that the logic board was replaced at some point. The s/n should have been addressed by the tech that replaced the board, though an inexperienced tech might not have the tools or know how to do that.

Or maybe there's some legit problem with the currently installed OS.

It's on the bottom of the stand. very faint small font.