Is it permissible to read the Quran up to the last part, then invite relatives to read the last part aloud in a group? Is there reward in that? Is there a prophetic hadith: "Whoever attends the completion of the Quran will have a supplication answered, either immediately or later"?

There is no harm in gathering family upon the completion of the Qur’an and supplicating with them, following the example of Anas ibn Malik (may Allah be pleased with him). However, singling out the last part for a collective recitation in one voice is an unlawful innovation (bid’ah), unless it is for educational purposes for those who cannot read well. The mentioned hadith about the virtue of the supplication of one who completes the Qur’an is weak and not authentically narrated from the Prophet (peace and blessings of Allah be upon him).