What should a person do who has missed many old prayers due to obsessive whispering (waswas), and then missed the Dhuhr prayer, and the time for Asr has begun? Should he pray Dhuhr and Asr? And what is the ruling for someone who missed a prayer like Fajr in this situation; should he pray it, or should he make up the oldest missed prayers first?

It is not permissible to abandon the current prayer to perform missed prayers. In this case, according to the Hanbalis, the order [of prayers] is waived for fear of missing the time of the current prayer. The preponderant opinion is that the order between missed prayers is a Sunnah, not an obligation, and this is the view of the Shafi'is. One who suffers from obsessive doubts can adopt this view to alleviate hardship. It is obligatory to ignore and turn away from obsessive thoughts.