Is it permissible to combine and shorten the Dhuhr and Asr prayers at home before traveling, or must Dhuhr be prayed at its prescribed time and then Asr be combined in Cairo? And is it permissible to perform the Sunnah prayers after shortening?

A traveler is not permitted to shorten the prayer until they have commenced their journey and left the village buildings, as Allah states: "And when you travel throughout the land, there is no blame upon you for shortening the prayer." If the time for Dhuhr prayer begins before departure, it is preferable to perform it. However, it is permissible to delay it and shorten it with Asr prayer after commencing the journey. It is also recommended to perform supererogatory prayers during travel.