Do the Duha prayer, the Fajr supererogatory prayer, and the Witr prayer fall within the supererogatory prayers, for which whoever prays twelve rak'ahs a house will be built for him in Paradise, or are the rak'ahs mentioned in this hadith independent of them, and is it possible to combine the intentions for these rak'ahs?

The twelve rak'ahs mentioned in the hadith refer to the regular Sunnah prayers (Sunan Rawatib). This has been explained in the narrations of the hadith as follows: four rak'ahs before Dhuhr, two rak'ahs after Dhuhr, two rak'ahs after Maghrib, two rak'ahs after Ishah, and two rak'ahs before Fajr prayer (the two rak'ahs of Fajr are "Ar-Raghibah"). These regular Sunnah prayers are more emphasized than other recommended Sunnah prayers, such as the Duha prayer and the Shafa' prayer. Shafa' is not an independent Sunnah, but rather it is linked to Witr.