How should a girl act towards her father when she has discovered that he is committing forbidden acts and speaking with women about sexual matters, and he does not respond to direct or indirect advice, and she fears that her silence about the truth may be a sin, while her mother and sister believe that they are helpless in dealing with him?

Searching your father's phone merely based on suspicion that he is talking to foreign women is not permissible. It is a form of spying, which is forbidden in Islamic law, as Allah says: ﴿O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. And do not spy﴾ [Al-Hujurat: 12]. And in the hadith: "Beware of suspicion, for suspicion is the falsest of speech. And do not look for others' faults, and do not spy." Accusing him of committing something forbidden merely because he is absent from home is a forbidden form of bad assumption. If the accusation is of adultery, it entails the severe threat of qadhf (false accusation of unchastity), and sincere repentance becomes obligatory. Honoring one's father is obligatory even if he does wrong. Among the greatest acts of honoring him is to supplicate for his righteousness and guidance. If you become aware of a wrongdoing he commits, advise him kindly and through a means that befits his status as a father. If he accepts the advice, then praise be to Allah. Otherwise, leave it. It is never permissible to abandon him, as that is a form of disobedience to parents.