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.
Celebrating the birth of the Prophet (Sallallahu Alaihi wa Sallam) is an innovation and not a Sunnah. Please refer to Fatawa: 81804 and 81920.
It is not permissible to put on a tape of recitation of Qur'an in the mosque and leave it for a whole night until Fajr.
It is also not permissible to do anything particular during the month of the birth of the Prophet (Sallallahu Alaihi wa Sallam), as it is forbidden to establish any ruling without any evidence in the Shariah. There is no proof that anything particular has to be done during the Mawlid (the anniversary of the birth of the Prophet (Sallallahu Alaihi wa Sallam)).
Allah Says (interpretation of meaning): {Or have they partners with Allâh (false gods), who have instituted for them a religion which Allâh has not allowed………}[42:21].
The companions and the righteous predecessors did not do so. If there is any good in it, they would have been the first ones to do it.
There is no harm in listening to the Qur'an while having sexual intercourse. What is forbidden though, is to move your tongue with the recitation (i.e. to recite with the tongue) during intercourse.
Al-Kharashi said: Al-Hattab reported from Ibn Al-Jawzi that the remembrance of Allah while relieving oneself or while having sexual intercourse by the heart is not disliked according to the consensus of the scholars.’
Allah knows best.