What is the ruling on greeting the maternal uncle and asking about him, given that he insults my beard and my family, expelled my father, openly commits sins, and slanders chaste women? Is he to be punished شرعًا (according to Islamic law) for his actions? And are we obligated to help people obtain their rights from him, considering that his actions are done in our name?

If your maternal uncle is as described, then he is in grave danger due to combining the severing of kinship ties, slandering chaste women, and openly committing sins. He must repent to Allah and mend his relationship with his relatives. If he insulted the beard intending to insult the law of Allah or the guidance of His Prophet, then he has exited the fold of Islam, and he must utter the two testimonies of faith, perform ghusl, and resume his Islam. As for the money he took unjustly, if he took it without authorization, he must return it; otherwise, his case must be referred to the competent authority. If he took it with your authorization, then you must fulfill the rights of the people, and then you have recourse against him. If he refuses, you may take from his properties an amount equivalent to what is owed.