All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
As for the first part of the question, there is no mention of such an act in the practice of the early Muslim generations; if it were a good deed, they would have done it. Verily, following the example of the early Muslim generations abounds in goodness and all evil lies in the introduction of religious innovation by the later generations. Hence, such an act is meaningless. We even fear that it might be the outcome of Satanic schemes aiming at distracting Muslims from what benefits them.
As for the second part of the question, we could not find an authentic Hadeeth indicating that Quran should be recited on the deceased’s body. However, Ma‘qil ibn Yasaar reported that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Recite the chapter of Yaaseen (no. 36) on your dead.” [Ahmad, Abu Daawood, and Ibn Maajah]
In fact, the authenticity of this Hadeeth is questionable; however, it is reinforced by other reports in the same vein. Such reports have been handed down on the authority of some Taabi‘een, including Safwaan ibn ‘Amr and Saalih ibn Shurayh Al-Koofi . The majority of scholars adopted that view and considered it recommended to recite the Chapter of Yaaseen on the dying person in particular. Ibn Katheer wrote, “One of the virtues and merits of this chapter, i.e. Yaaseen, is that reciting it eases one's hardships; and reciting it on the dead person calls for the descent of the mercy of Allaah and facilitates the release of the soul from the body.” [Tafseer Ibn Katheer]
Allaah Knows best.