Wanted to know about the so-called VIN numbers please?
Sure. VIN stands for Vehicle Identification Number, and there is some laws applicable to them.
I recently bought a car in a private sale, Is there anything i need to do with that?
You need to get the car's taxes calculated. For that, you and the seller need both to fill a form DTF-802,  so the DMV can do the taxes maths.
And in any case i need to register more than one vehicle?
That info can be located in any of the web pages listed on DMV's page.
Is there any proceeding involved in the eventuality i buy a car in NY and happens i wasn't a resident?
To fix that, please use form DTF-803, so you can receive a non-resident exemption from NYS sales tax.
Given i meet NYS requirements, i can register a vehicle, isn't?