Is it permissible to continue working at the university given the circumstances of not doing justice to the work and the low standard of education, provided that no explicit transgressions are committed? And if the answer is no, is it permissible to travel to work in a non-Muslim country?

There is no objection to remaining in the aforementioned job, and it must be performed as required, while striving to reform the institution and spread a spirit of diligence and perseverance within it through guidance and advice, and urging the management to do so, for perhaps Allah will rectify the institution's condition through your hands.