Does not performing ruqyah—despite the advice of scholars to do so—keep matters difficult, or is supplication sufficient to facilitate matters and relieve distress, and is the answering of supplication dependent on performing ruqyah?

Ruqyah is not a prerequisite for a prayer to be answered; it is a form of treatment and a supplication at the same time. Allah Almighty has guaranteed to answer whoever supplicates to Him, provided the supplication fulfills its conditions and is free from any impediments, as corroborated by His saying: "And your Lord says, 'Call upon Me; I will respond to you.'"