What is the ruling on money earned from working with a high school diploma, some of the exams for which were cheated on? And is working with it considered a breach of a covenant with Allah? What is the ruling on using this diploma to obtain higher degrees and work with them?

Repentance is obligatory for cheating in exams. As long as the person is qualified for the job and performs their work as required, what they earn from their salary is permissible (halal). Not abandoning the job obtained with the certificate is not considered a breach of covenant with Allah.