What is the ruling on a group gathering to read the Qur’an, study hadith, and preach to the household, where one of them intends to complete the Qur’an while the others study it, with each individual reading a part and correcting mistakes, and where there may be mixing between men and women, whether this takes place in the house of a living person or in the house of the deceased?

The gathering of people to perform a khatmah (recitation of the entire Quran) for the deceased, reading the Quran, and dedicating its reward, is an innovation (bid'ah). However, merely reading the Quran and dedicating its reward to the deceased, without gathering, feasting, or financial contributions, is permissible, and its reward reaches the deceased.

Similarly, there is no harm in people sitting in a circle to study the Quran or read Hadith. What is forbidden is the mixing of men and women without legal Islamic controls.

The principle is that the family of the deceased should be consoled with supplication and by preparing food for them. It is not appropriate to sit with them and eat their food, as the Companions considered gathering for the family of the deceased and preparing food after burial to be a form of niyahah (wailing/lamenting).

All good lies in following the Sunnah, and all evil lies in innovations.