Is it permissible to believe in God without believing in His names and attributes, especially the name and attribute of "The Most Gracious" (Ar-Rahman), given the difficulty of accepting it while a daughter suffers from cancer, and the questioning of the concept of divine mercy in such cases?

Belief in the names and attributes of Allah is a pillar of faith in Allah, and denying the name "Ar-Rahman" (The Most Merciful) or His attribute "Ar-Rahmah" (Mercy) is disbelief in Him. The suffering and illnesses of creation do not contradict Allah's mercy; rather, they are for a wisdom that He, glorified be He, knows, which we may or may not comprehend. Among these wisdoms in the affliction of children with pain are compensation for them after their death, a lesson for adults, and a reward for parents. Moreover, the crying and screaming of children have health benefits for them in expelling moisture from their brains and strengthening their nerves. A Muslim should exert efforts to seek healing, such as visiting doctors, performing ruqyah (definition) (Islamic exorcism/healing), and supplicating, and should not despair of Allah's mercy, for every disease has a cure.