All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We do not know any evidence from the Book of Allaah, or the Sunnah of the Prophet or a saying of a companion which suggests that it is forbidden to turn one's back towards the Qiblah. However, there is evidence in the Sunnah about the Imaam turning his back towards the Qiblah after the prayer. 'Aa'ishah narrated that: "When the Prophet prayed he did not remain in his position except for the period of time he says: "Allaahumma antas-salaam waminkas-salaam, tabaraktaa yaa thal-jalaali wal-ikraam." [O Allaah, You are As-Salaam (which implies the One Who is free from all defects and deficiencies) and from You is all peace, blessed are You, O Possessor of majesty and honour." [Muslim] Moreover, Samurah Ibn Jundub said: "Whenever the Prophet completed leading Fajr prayer with us, he would turn towards us." [At-Tirmithi] The Prophet turning his face towards the people after the prayer means that he turned his back towards the Qiblah.
Nonetheless, Imaam Ahmad disliked for a person who is sitting in the mosque to turn his back towards the Qiblah. It might be that the reason he disliked this is that the person who sits in the mosque should engage himself in reading the Quran or mentioning Allaah, in which case it is recommended to be sitting facing the Qiblah. If he turns his back to the Qiblah, he loses the merit and excellence of facing the Qiblah. Abu Hurayrah narrated that the Prophet said: "Everything has a master, and the master (i.e. the best) of sitting is by sitting facing the direction of Qiblah." However, we do not know any evidence that it is disliked to turn one's back towards the Qiblah in other places than the mosque and in circles (of mentioning Allaah).
Some scholars disliked putting the feet towards the Qiblah as a sign of glorification and exaltation to it. Yet, it should be noted that the dislikeability is a religious ruling which has to be supported by evidence from the Book of Allaah, or the Sunnah, or correct analogy, or consensus of the scholars and we are not aware of any evidence that it is dislikeable to put one's feet towards the Qiblah.
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Allaah Knows best.