Q 2: Is it permissible for a Muslim to
supplicate to Allah (Exalted be He) by His Names to cure diseases?
It is permissible to do so according to Allah's saying,
And (all) the Most Beautiful Names belong to Allâh, so call on Him by them
This was also authentically reported from the Prophet (peace be upon him). He made Ruqyah (reciting Qur'an and saying supplications over the sick seeking healing) for some people by saying,
O Lord of the people! Remove the difficulty and bring about healing as You are the Healer. There is no healing but Your Healing.