Does a Muslim receive the reward of a complete Hajj and Umrah if he recites the adhkar in his home after Fajr prayer until sunrise and Duha prayer, or must this be done in the mosque to attain this reward?

The Hadith indicates that the reward of a complete Hajj and Umrah is attained by one who prays Fajr in congregation, then remains in his prayer place remembering Allah until the sun rises, then prays two rak'ahs. This virtue is specific to one who remains in his place. As for someone who goes home, remembers Allah, and prays Duha, he will receive much good, but most likely, he does not fall under the virtue of this Hadith.