Целесообразно ли выполнять упражнения при наличии Синдром Хронической Усталости? Какие упражнения Вы бы порекомендовали и насколько они должны быть интенсивными?

This depends on the severity of your symptoms. Obviously if you stop all activity your fitness will decline and so your body will find it more tiring to do things, therefore I believe that people with ME should do activities by stop before they feel tired. This will take some experimentation to see why that point is. You should not push yourself to do more as this will lead to days of inactivity while you recover. Try to maintain a lower level of activity every day rather than a very active day followed by days of no activity.