Is a prayer considered performed on time and not a make-up if it was completed exactly at its due time (6:12:00) while its actual completion was a few moments later (perhaps 6:12:30), and is a person suffering from obsessive-compulsive disorder sinful for delaying the prayer due to repeatedly performing ablution?

It is not permissible to delay the prayer without a valid excuse until its time is almost over. Whoever catches one rak'ah before the time expires has performed the prayer on time. It is obligatory to combat and treat obsessive-compulsive disorder (waswasah). As for the person afflicted with waswasah who struggles against it but is overcome, and thus prays after the time has expired, it is hoped that they will be excused.