Is intention required for a vow (nadhr), and does masturbating by looking fulfill the condition of a vow that necessitates fasting?

A vow of persistence and anger (Nathr al-Lajaj wa al-Ghadab) is treated like an oath (yamin). The one who made the vow has the choice, according to the majority of scholars, between fulfilling the vowed act or offering an expiation for an oath (kaffarat yamin). The basis of a vow is the intention of the one who made it. If he intended repetition, then the vow is repeated with the repetition of the condition it is tied to. If by "masturbation" you intended masturbation by hand, then your vow does not include masturbation by other means. As for "looking" (al-nazar), if it is intended to cause the emission of semen, then it is considered masturbation; otherwise, it is not.