Thank you for all the advices.
Well, it's done now so I'm just hoping nothing goes wrong. What really got me nervous was when he told me he didn't have the MOT certificate, no V5, etc. This way, I wouldn't be able to even get the V5C/2 section.
Because actually he's intention was to remove the private plate first and then sell me the car. But it's me who needs a car like NOW. Using my head, maybe I should get another car. But using my heart, and after driving this car...
By the way Kenny, do you also work very close to Paisley?