Is it permissible to donate a copy of the Qur'an as an ongoing charity (Sadaqah Jariyah) on behalf of my living mother, provided I purchase it with my own money, and does this require the permission of the mosque administration?

Donating a Qur’an as a waqf (endowment) is permissible, and it is permissible to gift the reward of any ongoing charity (sadaqah (definition) jariyah) or good deed to a living or deceased Muslim. So, if you intend to dedicate a Qur’an from your own wealth as a waqf for your mother, this is valid and considered an act of righteousness towards her. You may place the Qur’an in the mosque without needing permission from the mosque’s administrator.