How does someone with obsessive thoughts pray? And does the principle of ease in religion apply to him, given his suffering from obsessive thoughts related to ablution and prayer, and the impurity of donkey feces, dry urine on the bed, and pre-seminal fluid spread throughout the house? And what should he do if he abandons prayer because of this suffering?

The fundamental principle regarding things is purity. Nothing is deemed impure unless there is certainty that impurity has transferred to it, and impurity does not transfer from a dry object to another dry object upon contact. What is mentioned in the question about clothes becoming impure from donkey dung, or impurity transferring to mobile phones and light switches, is nothing but whispers from Satan. Abandoning prayer is impermissible under any circumstances. It is advised to strive against one's own self, distract oneself from these whispers, not indulge in them, seek Allah's help, and present the case to mental health specialists.