Is it permissible to spend money acquired from government work, which is a mixture of lawful and unlawful, on building mosques to purify the car bought with it, instead of returning it to the state treasury where it is feared it might be stolen?

Leaving work before the end of working hours without permission is impermissible. The salary you receive as a result of this is not rightfully yours, and you must return it to your employer. If direct return is difficult due to fear of theft, you may spend it on public welfare for Muslims, such as mosques and hospitals. The car is your property, and there is no harm in benefiting from it.