Is it permissible to swear an oath to abandon watching pornographic websites in order to help oneself overcome this sin, and is expiation obligatory for one who breaks this oath, and is the perpetrator of that considered a "muḥṣan" who has committed "fāḥishah"?

It is permissible for a person to swear by Allah to seek help in abandoning a sin, but excessive swearing is prohibited, and expiation is required if one breaks the oath. Viewing forbidden things is a great sin for everyone, and its sinfulness increases for a married person because he has been provided with lawful means to abstain from unlawful ones. However, viewing forbidden things is not considered equivalent to committing indecency that necessitates a legal punishment.