What is the ruling on purchasing a private car for the site from the monthly discounts on the contractor's payments or from the spare parts budget exceeding the need, and registering it in the manager's name, while the manager uses it for personal purposes?

In this work, you are considered a private, trustworthy employee. You must observe trustworthiness and adhere to the specified tasks. You are not permitted to purchase a car for the project without authorization, even if you believe you deserve it, because you are an agent and are not entitled to deviate from what your principal has stipulated for you, and "Muslims are bound by their conditions." If you are authorized to purchase a car or are given a general authorization that includes it, then you may act in a way that benefits the work and use the car according to regulations or custom. If its use after working hours is permitted, then there is no harm; otherwise, it is not permissible.