Does a vow to abandon masturbation—which is toying with the hand or inserting something into the vagina to reach climax—include masturbation by thinking or by rubbing any object from the outside? And does the vow necessitate fasting every time semen is discharged? And what are the consequences of repeating the act at the same moment?

This vow is called a vow of obstinacy (Nathr Lajaj), and the preponderant opinion concerning it is that its maker has the choice between fulfilling it or not fulfilling it, while paying an expiation for an oath (kaffarat yamin (definition)). What is considered in vows is the intention and purpose of the one making the vow. The questioner explicitly stated that her intention from the vow was jesting or inserting something into the private part. This does not include masturbation by thinking or by something external; the consideration is the insertion of something into the private part, not the emission of semen. If the insertion of something into the private part is repeated, along with the emission of semen and the attainment of the desired pleasure each time, then fasting is obligatory for each instance.