Is obsessive-compulsive disorder considered a legitimate excuse that relieves the person afflicted by it from the blame for falling short in some of the pillars and duties of prayer and ablution, based on the Almighty's saying: "nor upon the sick any [strict] requirement"?

The cure for waswasah (obsessive whispering) is to ignore it and not pay attention to it. So, no matter how much Satan whispers to the one afflicted with waswasah that he did not perform such-and-such from the obligations of prayer or ablution, he should disregard it unless he attains absolute certainty of having omitted it. Ibn Taymiyyah's statement confirms that waswasah disappears with seeking refuge [in Allah] and remaining firm upon the truth, for if Satan sees the servant's strength and steadfastness, he will depart from him. Allah's saying: "Nor is there any hardship on the sick" (24:61) includes the one afflicted with waswasah, because he is sick. He is commanded not to yield to his waswasah, and if he does so, he has fulfilled his duty. There is no basis for specifying a period of twenty-one days for ignoring it; rather, the one afflicted with waswasah should continue to ignore it until Allah grants him recovery. If the matter reaches absolute certainty, then the one afflicted with waswasah is like anyone else; he is obliged to rectify what he is certain he omitted, such as the presence of impurity or the omission of a pillar or an obligation.