Is it permissible to combine the intention of fasting the three days of the month with fasting the Day of 'Arafah with a single intention, and will that result in receiving the reward for both fasts?

The overlapping of acts of worship is of two types:

The first type: where overlapping is not permissible. This is when the acts of worship are intended for themselves or are subordinate to others, such as the Sunnah prayer of Fajr not sufficing for the Duha prayer, or vice versa; or the intention for the obligatory prayer and the ratiba (supererogatory regular prayer) in the Fajr prayer not sufficing with a single intention.

The second type: where overlapping is permissible. This is when the intention behind the act of worship is merely the action itself, and the act of worship itself is not primarily intended, such as the obligatory prayer upon entering the mosque sufficing for the greeting of the mosque (Tahiyyat al-Masjid), or the Duha prayer sufficing for the greeting of the mosque. It is more complete to intend both.

This also applies to fasting. If the fast of the Day of 'Arafah coincides with the intention of fasting the three days of each month, it suffices for it. It is better to intend all of them.