Is communal supplication permissible after completing the recitation of the Qur’an, and is it permissible to honor guests who attended the completion of the Qur’an with a dinner meal?

There is no harm in honoring the worshippers and guests of the mosque on the night of the Quran's completion, as long as it does not involve extravagance or ostentation, and as long as it does not take on the character of an act of worship specifically associated with the completion. If there is a fear that it might become associated with it in people's minds, to the extent that some might consider it a means of drawing closer to Allah specifically at that time, then it is prohibited, as it would fall under the category of an "additional innovation" (bid'ah idafiyyah).