Is there anything in the Qur'an or the Sunnah about any customs after finishing of the reading of the Qur'an (Khatm Qu-ran) like cooking special food or reading special Du'a?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Supplication is legal and recommendable when a person finishes reciting the whole Holy Qur'an, since this is proved and was done by The Prophet's companions.
Al-Darimi reported from Thabit al-Banani who said: 'Anas Ibn Malik used to gather his children and his family after finishing recitation of the whole Qur'an, and then, to make supplication on their behalf.'
Yes, there is no objection to give a banquet as a form of thanking Allah for the blessing of finishing the recitation of The Holy Qur'an. But, it becomes an innovation if one believes it is Sunnah.
Allah knows best.