What is "Telei Chalav"?
Radak: It was still nursing.
Why is "va'Ya'alehu" written without the Vov at the end?
Rashi (from Avodah Zarah 24b): It is written like va'Ya'aleha, to teach that it was a female. Chachamim inferred that a female is Kosher for an Olah on an individual's Bamah.
How could Shmuel offer a Korban? He is a Zar!
Radak: (When Mishkan Shilo was destroyed, the Mishkan came to Nov and Bamos were permitted. 1 - Zevachim 118b) Chazal inferred that a Zar may offer on a Bamah (Avodah Zarah 24b).
Radak citing Vayikra Rabah 22:9: Bamos are permitted [after they were forbidden] only via Navi. Shmuel was the first to offer on a Bamah after Shilo was destroyed, and Yehoshua was first to offer in Gilgal - "Az Yivneh Yehoshua" (Yehoshua 8:30).
How did Hashem answer him?
Radak #1: Perhaps fire descended from Shamayim on the Olah.
Radak #2: Hashem sent thunder with a great noise to befuddle the Pelishtim. When he heard this, he knew that Hashem answered him. Malbim, from Toras Kohanim (Vayikra 1) - Hashem's voice to a Navi separates onto many paths. With the same "Kol Hashem Shover Arazim" as at Sinai, Hashem answered Shmuel. Yisrael did not hear, but it was thunder for the Pelishtim and befuddled them (verse 10).