Is it permissible to combine the intention of "greeting the mosque" (tahiyyat al-masjid) with the intention of Salat al-Istikhara or Salat al-Hajah in one prayer, and does this apply to Salat al-Shaf' (the even-numbered rak'ahs of Witr)?

The mosque greeting (Tahiyyat al-Masjid) is performed by two independent Rak'ahs, or by performing an obligatory (Fard) or supererogatory (Nafl) prayer. It is not a condition that two independent Rak'ahs be prayed. If a Muslim prays two Rak'ahs with the intention of a regular Sunnah or a non-regular Sunnah, or performs the obligatory prayer, this suffices and he has achieved the mosque greeting. As for other prayers such as Istikhara prayer (prayer seeking guidance), Sunnah of Wudu (ablution), and regular Sunnah prayers, the mosque greeting does not suffice for them. Rather, they are only fulfilled by performing each of these prayers independently.