I know the anime is not the same as the game and makes stuff up, but is there ever any mention of physical and special stats and which attacks belong to one of them? Did they also change it later on?

If you can afford fixing it up do it then you idiot. Do you even have anything important to spend your money on? Unless you are married and have children or run an actual bussiness, the extra money you make SHOULD be going into getting this car rolling again.
I plan on getting a 7 series to fix up myself in a few year(s) when I am comfortable with my current income and have a daily that I wont have to worry about failing