Is it permissible to continue reading parts of the Qur’an and distributing them among participants in a study circle for a communal recitation (khatm) of the Qur’an for the purpose of encouragement? Is this considered an innovation (bid‘ah) or a good practice (sunnah hasanah)? Is it permissible to recite the du‘a’ (supplication) for completing the Qur’an after this communal reading? And what is the ruling on doing that for the deceased?

What you are doing by each reading only one juz' (part) is not considered a complete recitation (khatm) of the Qur’an. Also, the aforementioned supplication is not considered a supplication for completing the Qur’an. The advice is to form a study circle where you can gather to memorize and study the Book of Allah. This should take place in a mosque so that you may fall under the meaning of the hadith: "No group of people gather in one of the houses of Allah, reciting the Book of Allah and studying it among themselves, except that tranquility descends upon them, mercy encompasses them, angels surround them, and Allah mentions them to those with Him." If you gather in the mosque, there should be a barrier between you and men. Each of you should be keen on memorizing the Book of Allah and regularly reciting it. Gathering to complete the Qur’an and dedicating its reward to the deceased is one of the newly invented innovations (bid'ah muhdathah) that must be abandoned, and participation in it is impermissible.