Why did the Navi ask Achaz to request a sign?
Rashi: I 1 know that you do not believe Hashem's word.
Radak: He knew that Achaz did not believe Hashem's word. He himself proved this - he sent messengers to Melech Ashur, and asked him to save him from Melech Aram and Melech Yisrael (Melachim II, 16:7), and sent a bribe to him! Malbim (12) - this was a pitfall for him and Yehudah. This caused Melech Ashur to repeatedly come to Yehudah!
Since this was a Nevu'ah from Hashem, presumably, 'I' refers to Hashem. However, Rashi's words imply that 'I' refers to Yeshayah. (PF)
Why did he say "Elokecha"? Achaz did not believe in Hashem!
Radak: He is your G-d, and He worldly judge [and save] you from these kings. Believe in Him, for He is Elokim - Master, Supervisor and Judge!
What is the meaning of "Ha'amek She'alah [Oh Hegbe'ah l'Ma'alah]"?
Rashi: Descend deeply and ask. This is [a command,] like "Shima'ah? Selachah" (Daniel 9:19). Request a sign in the depths, to revive a Mes for you, or raise above, to request a sign in Shamayim.
Radak: Ask anything that you want. Ha'amek is Makor (infinitive) conjugated like a command, like "Hashem Shima'ah Hashem Selachah."
Radak citing Targum Yonasan: Ask that a miracle be done for you on the land, or you will see [a sign] in Shamayim. Radak - he translated 'miracle' regarding the land, for the sign that he gave to him in the land was via a miracle, that a baby had Da'as and recognition.
Malbim: Ask that He change a matter of the Yesodos (foundations, or 'elements), or a sign in Shamayim, like the sun stopping. One who requests a sign, it is so he will believe, or so others will believe. If you request for yourself, it suffices in the land; it is good to minimize the miracle. If you ask so others will believe, [ask] above, so it will be publicized to the Rabim.