What is the ruling on reciting the Qur’an for the deceased and placing the Mushaf on his abdomen, and are there specific days for mourning?

Reading the Quran for the deceased or at the grave is an innovation (bid'ah) and has no sound basis, and so is placing the Mushaf on the deceased's stomach. As for offering condolences, it is legislated from the moment the soul departs and has no specific time limit in the Shariah; it is permissible in any place.