Is it permissible to demand financial compensation from the maternal uncle for psychological damages resulting from his actions that led to failing an exam, in order to mend the relationship between the two parties while preserving kinship ties, and what is the ruling of Islamic law on that?

We advise you to forget the old matter with your uncle. You have blown it out of proportion. Even though your uncle entering without permission is not permissible, even if it is his sister's house, and your father's consent to his visit is what matters, you alone bear the consequences of your failing the exam. Problems exist in every home, and the wise person is one who acts properly. You should not continue dwelling on the past to avoid psychological pain. Rather, forget the matter and attend to your work, maintain kinship ties, and advise those who err. Do not consider demanding financial compensation from your uncle to avoid a family rift, and let mercy overcome anger.