I know it looks like the bride and groom are reading something, but I think it's the aarsi-musaf. Usually, a mirror is placed on the Quran and the groom sees the bride for the first time in the mirror. There is a second step, where the groom reads/recites a surah and writes the surah (using sandalwood powder) on the bride's forehead.
But, I could be wrong...
Yup. I don't remember it being on top of the Quran, but I do think it's a very nice tradition.