Is kaffarah obligatory for someone who breaks their fast in Ramadan due to masturbation during the day, or due to a wet dream followed by a severe feeling of thirst and hunger? And is it permissible to consider fasting on Mondays and Thursdays as kaffarah for those days?

You must make up for the days you missed. There is no impediment to combining the intention of making up the fast with fasting on Mondays and Thursdays. Expiation (kaffarah) is obligatory, according to the majority of scholars, for sexual intercourse during the daytime in Ramadan. There is also an expiation for whoever delays making up for Ramadan without a valid excuse until the next Ramadan begins, provided he knows the impermissibility of delaying the make-up fast. This is also according to the majority of scholars. It is advisable to increase good deeds, such as fasting and others.