Is the monthly grant and the professorship salary permissible after what I mentioned regarding consultations about the graduation project, and have I been acquitted of responsibility before Allah, especially with my anxiety about the answer from Islamweb?

There is no harm in studying at a teacher training center and benefiting from the scholarship. One must disregard the [baseless] misgivings related to this matter and perform the assigned work as required. In that case, there is no harm in benefiting from the salary.