How can a repentant girl, who engaged in sexual acts via the internet and phone, mend her ways, escape the harshness of her guardian, and obtain a lifeline after her father refused her marriage?

There is no rest or tranquility for the heart except in obedience to Allah. The acquaintance between non-mahram men and women is impermissible due to the fitan (trials/temptations) it leads to. One must repent and sever forbidden relationships. The father should marry off his daughter if a righteous suitor proposes to her. It is not permissible to delay marriage on the pretext of education; rather, this is considered adh'l (preventing a woman from marrying) which is prohibited. Until marriage, one must hold fast to Allah, strive in acts of obedience, avoid fitan, be keen on learning the religion, choose righteous companionship, and be persistent in supplication.