Is it obligatory for someone who is fasting for two consecutive months as an expiation to fast on the Day of Arafah if it falls on the 33rd day of their fast, or must they break their fast? And do they resume fasting from where they stopped?

Fasting the day of Arafah is not forbidden; rather, it is legislated for those who are not performing Hajj. If someone is fasting for two consecutive months and their fasting days coincide with the day of Arafah, they must complete it. If they break their fast on that day, the continuity is broken. As for Eid day, breaking the fast is obligatory, but the continuity is not broken by breaking it on that day. Similarly, the continuity is not broken if the obligatory fasting is interrupted by fasting Ramadan, or by an obligatory breaking of the fast such as Eid al-Fitr, or menstruation, or postpartum bleeding (nifas), or a frightening illness, or the breaking of fast by a pregnant or breastfeeding woman.