can unbalanced 3 phase load make meter run faster?

I understood he is connected at the input panel of the building entrance, downstream from the utility meter. His power meter is used only for the landlord to charge him his electrical consumption.

1. I am sure this installation is undersized & unsafe.
2. Unbalanced three phase load is not dangerous in itself if properly protectected upstream by the right size three phase breaker. However, this very breaker is going to trip when the first phase reaches the limit, thereby cutting off power to all your load.
3. As for the meter running faster i.e. indicating more electrical consumption, I doubt any one of us can answer without specifics you haven't provided, and apparently you're not qualified enough in this domain to describe.
4. Stick to your computer business and hire a qualified electrical contractor.
5. Have you heard of Business Impact Analysis, it only means what will it cost you if the cheap ad hoc electrical job fails ?

My humble guess is many times more the cost of a proper electrical installation.

Tommy