Q 1: It is narrated in a Hadith from the Prophet (peace be upon him) that he said:
Whoever prays the congregational Salah 'Prayer' of Fajr 'Dawn', then sits 'in the Masjid [mosque]' doing Dhikr 'Remembrance of Allah' until sunrise, then prays two Rak`ahs 'units of prayer', receives a complete reward of Hajj and `Umrah 'lesser pilgrimage'.
My question here is whether these two Rak`ahs are considered a part of Salat-ul-Duha (supererogatory Prayer after sunrise) which is to be performed in eight Rak`ahs, or are they another independent Nafilah (supererogatory) Prayer?
The two Rak`ahs which are mentioned in this Hadith are considered a part of Salat-ul-Duha though they have special merit due to being linked to sitting in the Masjid until sunrise.
On the other hand, the best time for offering Salat-ul-Duha is when it becomes very hot in the forenoon.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.