Why did he request a sign that he will be healed?
Radak (Melachim II, 20:8): The decree was double - "Mes Atah v'Lo Sichyeh" (verse 1). He thought that Yeshayah is merely consoling him, for he saw that he cried greatly. Even though he saw that the boil healed 1 , he did not think that he will be strong enough to enter Beis Hashem. Perhaps the boil had not yet returned [to be like totally healthy flesh], or the illness had not departed from him.
Malbim: He said, after a miraculous cure (via pressed figs, which normally harm boils), no sign is needed. Yeshayah said, Hashem prepared a greater sign, which will be a miracle for nations.
This was a double miracle! Perhaps he thought that it was because Yeshayah said so - "va'Sigzar Omer v'Yakam Lach" (Iyov 22:28), but Hashem would not heed him against His decree. (PF]
Did he request another sign after the sun went back (verse 8)?
Radak: The sun went back to fulfill his request for a sign; this is written out of order.
