My mother-in-law bought us a car. Do we need to pay some money? How is it appropriate?

There is no fixed standard for such a thing.

As long as everyone is willing, it doesn't matter who pays and who pays more.

If her mother-in-law has superior conditions and this enthusiasm, then she can receive a gift from her mother-in-law.

If the mother-in-law is in a bad condition, then consider giving some money yourself, or not letting her out.