Is it permissible to search a sister's phone and monitor her conversations out of concern for her, and is this considered a sin? What is the Sharia's advice for a sister who is in an illicit relationship and refuses the advice of her family?

Searching a sister's phone without her permission is forbidden because it is a form of spying, and one must repent and apologize to her. A sister's ill-treatment of her parents is among the major sins. If the sister has an illicit relationship with a young man, she must repent and cut off the relationship. However, if the young man is suitable and proposes to her, and she agrees, the father has no right to prevent her from marrying him; otherwise, he would be a 'āḍil (one who unjustly prevents marriage).