1)
Did Nebuchadnetzar remember the dream?
1.
Rav Sadya Gaon: Yes! If not, he would not have believed Daniel's interpretation. He did not tell the Chachamim, in order to test them.
2.
Ibn Ezra: No. It says "va'Tipa'em Rucho Lada'as Es ha'Chalom"! Once Daniel told him, he remembered.
2)
Why was he so anxious to know the dream?
1.
Malbim: He knew that it foretells the future. Refer to 2:1:4:3.
