1)
Why did his scarf fall from him?
1.
Radak (11): It was in order that Elisha would be able to use it to split the Yarden (verse 14).
2.
Malbim: This is the scarf in which he wrapped his face in the cave [when Kevod Hashem passed], and through it he split the Yarden. It fell now because Eliyahu was stripped of partitions and garments 1 , and he wore Kodesh.
1
Radak: If so, why didn't his other garments fall? (Perhaps Malbim holds that indeed, they all fell; Elisha took only the scarf.)