Is it permissible to hold mourning gatherings and offer collective supplications for the deceased in the mourner's home, and is it permissible to hold a "Khatmah" (recitation of the entire Quran) in the mosque?

There is no evidence for the permissibility of reciting chapters from the Quran in the place where the deceased passed away or resided, nor was this transmitted from the Companions or their successors. The basic principle is prohibition, based on the Prophet's (peace be upon him) saying: "Whoever performs a deed not in accordance with our matter, it will be rejected." Furthermore, gathering to supplicate for the deceased after the funeral prayer is an innovation (bid'ah), as this was not authenticated from the Prophet (peace be upon him). What is authenticated from him is standing by the grave after burial and saying: "Ask for forgiveness for your brother, for he is now being questioned." Therefore, one should supplicate for the deceased individually. It is permissible to supplicate for him during prayer and outside of it, at times when supplications are answered, with sincerity in the supplication.