Who was Chuldah?
Radak, from Megilah 14b: She was a descendant of Rachav 1 .
The Gemara says also that she was a relative of Yirmeyah.
Why did the king send them to Chuldah, and not to Yirmeyah?
Rashi, from Megilah 14b #1: A woman has more mercy than a man.
Rashi, from Megilah 14b #2: Yirmeyah was not there. He went to return the 10 tribes.
Radak: Even though Yirmeyah's Nevu'ah started in Yoshiyah's 13th year, and this was his 18th year, Yirmeyah was not in Yerushalayim at the time, or he was fasting 1 when they found the Torah. Chuldah sat in Yerushalayim. Three prophesized in Yoshiyah's days - Yirmeyah in the markets, Tzefanyah in the Batei Kenesiyos, and Chuldah to the women (Pesikta Rabasi 26).
Why is this a reason not to send to him? Perhaps the king assumed that he is not amidst Simchah while fasting, and will not receive Nevu'ah (PF).
Which garments did he guard?
'Rashi' (Divrei ha'Yamim II, 34:22) #1: He guarded Bigdei Kehunah.
'Rashi' (Divrei ha'Yamim II, 34:22) #2: He guarded royal garments.
What is the meaning of "b'Mishneh"?
Rashi #1: It is a Beis Midrash (and so says Targum Yonasan). There is a gate in the Azarah called Sha'ar Chuldah (Midos 34a). Hagahas R. Ovadyah ha'Navi - she would teach oral Torah, i.e. Mishnah, to Chachamim of the generation 1 . Hagahas Sod Meisharim - she taught [Mishneh Torah, i.e. all of Sefer Devarim] from "Elu ha'Devarim" until "l'Einei Kol Yisrael." She taught the punishments for those who transgress the explicit [laws], and those who transgress the secrets and hints in the Torah.
Rashi #2: There were two walls of Yerushalayim; she sat between them.
Alei Tamar (Kidushin 4:11): Surely the Beis Midrash was only for women, like Pesikta Rabasi 26 says that she prophesized for women. From the days of Devorah, there was a Beis Midrash for women (Targum Yonasan, Shoftim 5:24). (The Targum did not say that the Beis Midrash was for women! Devorah taught Torah to Rabim (Tana d'Vei Eliyahu 10), and sat under a palm tree to avoid seclusion (Megilah 14a). If she taught only women, she could sit in a house! Tosfos (Nidah 50a) says that she did not judge; she taught the laws [i.e. to men, and they gave the verdict!] - PF)