Is it permissible to take the monthly transportation allowance from the Ministry of Education, even though the use of a private car for transportation between schools is very infrequent?

What governs this is the contract between you and your employer. If the transportation allowance is given to the employee regardless of their actual expenses, then there is no sin upon you in benefiting from any remaining money once you have completed your task. However, if your employer grants the employee only what is needed for their transportation expenses, and any excess must be returned, then it is not permissible for you to keep the remainder. Instead, you only own what you have spent for the purpose of work. The former scenario is the more common understanding, and it is easy to ascertain the entitlement by referring back to the employer.