Is the intense fear of diseases—especially cancer—and its causing a lack of devotion in prayer and remembrance of Allah, a psychological illness or a whisper from Satan? Are there any supplications to get rid of these worries?

The source of fear is Satan, therefore, one must seek refuge in Allah from him. Satan has no authority over those who believe and who put their trust in their Lord. Prevention from worries and sorrows is through faith and righteous deeds, and their cure is through the established Prophetic supplications. One must repel Satan's whisperings by relying on Allah, for the plot of Satan is weak.