Is it permissible for someone who feels air escaping during ablution and believes they are afflicted with obsessive-compulsive disorder to pray an invalid prayer, and must they repeat the prayers they missed because of that?

There is no cure for obsessive-compulsive disorder (waswas) except to ignore it. If you are afflicted by it, do not pay attention to the devil's whispers about passing wind or clothes becoming impure, unless you are certain. Proceed with your acts of worship and prayers without repeating them, and do not change your clothes merely due to whispers, for the default state of clothes is purity. If a garment becomes impure, wash only the affected area.