What is the ruling on giving one's sister a phone to speak with a person with whom the relationship is still unofficial (only the Fatihah has been recited), especially given that they are secluded together and the father deliberately leaves them alone? Is it permissible to leave the apartment if these forbidden acts continue?

It is permissible for your sister to be given a phone to speak with her suitor if the call is out of necessity and adheres to শরীয়াহ (Islamic law) guidelines. However, if it is not out of necessity or exceeds the boundaries of শরীয়াহ, then it is not permissible. It is not permissible for your father to allow your sister to be in khalwa (private seclusion) with her suitor. You must sit with them, or bring someone whose presence would prevent khalwa. Removing the niqab (face veil) in front of the suitor, without khalwa, is not permissible. You are not required to leave your father's house due to the violations, but you must persist in enjoining good and forbidding evil with gentleness and politeness towards your parents.