Is it permissible to face away from the Qibla in the mosque, given that the worshipers turn towards the face of the one facing away during their supererogatory prayers? And is it true that a face towards which one prays will not prosper?

The default ruling is that it is permissible to turn one's back to the Qibla, whether inside or outside a mosque. Scholars have based this on the hadith of Abraham (peace be upon him) leaning his back against Al-Bayt Al-Ma'mur (the Frequented House). Based on this, it is permissible for you to turn your back to the Qibla in the mosque, even if people are praying in your direction. As for the narration you mentioned concerning this matter, it has not been found. However, if this act contradicts good manners (murū'a) or distracts a worshipper, then it should not be done.