Here is my 5c on the matter - not to be taken as being credible as I am not there in person and could be missing other vital signs
First thing you could do is run the engine with the original belt in place and SC belt removed, you will probably find its all running sweet - maybe try it and find out.
A gear drive supercharger can absolutely make these kind of wild sounds and be totally fine, it is a noise that becomes worse the more unevenly the engine runs/fires at lower rpms, you can see on the vid that with a few rpm the weird noise more or less goes away. Basically the more smoothly the engine runs the less the gears in the charger will chatter.
About the oil in the charger, you need to learn ASAP how much oil the charger needs to have in it, how to check it with certainty, what grade of oil and how often it needs to be serviced. That type of charger doesnt have an oil container as such, it has either level bung in the transmission that you open and see if any runs out or it has oil supply from the engine itself. If you do stuff up and run the charger low on oil, then have a couple of thousand dollars ready for the repair, a gear set is hyper expensive and there arent any second hand pieces available at all
Could be all ok, or maybe not, I have put forward some thoughts and you can ask other people for their opinion as well - so long as they are someone who has worked with superchargers