Is expiation obligatory for one who returns to watching pornography after having promised Allah to desist, and will he be punished for that, and how can he rid himself of this sin?

An oath taken on the Mushaf is a binding oath (yamin mun'aqidah) that necessitates a single expiation (kaffarah). This expiation involves feeding ten needy persons or clothing them. Fasting is only permissible if one is unable to do either of these. As for a promise made with the word "covenant" ('ahd), there is a difference of opinion regarding the obligation of expiation if one breaks it; however, the more cautious approach is to pay it. Using oaths to abstain from sins is not a sound approach. The straight path is to seek Allah's help and offer sincere repentance (tawbah nasuh) by abandoning the sin, regretting it, and resolving never to return to it. A valid repentance erases what came before it, and one who repents from a sin is like one who has committed no sin.