Is there a specific supplication (du'a) before reading or memorizing the Quran? And are ablution (wudu) and covering the 'awrah (including the head for women) obligatory before touching the Mushaf and reading from it?

There is no specific supplication (du'a) prescribed before reading or memorizing the Qur'an. However, it is prescribed to seek refuge with Allah from the accursed Shaitan (the devil) before recitation. There is no harm in supplicating for ease of memorization and understanding at any time. It is not a condition for a woman to cover her head when reading the Qur'an, nor is ablution (wudu') required except for touching the Mushaf (definition) (the physical copy of the Qur'an). It is recommended to glorify the Qur'an and to recite it with contemplation and humility in all circumstances.