Who will rejoice in Hashem?
Radak citing Targum Yonasan: Yerushalayim says, I will rejoice in Hashem's word.
Radak: Yisrael will say so when they return from Galus. My father says, "ba'Shem" is in Midas ha'Rachamim.
Why does it add "Tagel Nafshi bEi'lokai"?
Radak: This is Midas ha'Din. Here it mentions the Nefesh, for it is supreme and accepts afflictions more than the body does. Regarding Hashem (Midas ha'Rachamim), both the body and Nefesh rejoice.
Malbim: Sisah is external actions to show Simchah; he will outwardly rejoice in Hashem, who created everything. Gilah is rejoicing of the heart over a new good that he did not hope for until now, i.e. it was revealed to me that He is Elokai (has special Hashgachah Pratis over me).
What are "Bigdei Yesha" and "Me'il Tzedakah"?
Radak: This is a metaphor. Begadim clothe a person, and he wraps himself in a Me'il. Therefore, "Ye'atani" applies to it.
Malbim: Begadim are worn underneath. They are sewn according to his size. Me'il is used to wrap himself and wear over his garments; it is not sewn according to his size. Hashem will clothe me with His salvation 1 . It will be like an undergarment sewn to my size, i.e. an individual salvation special for me alone. Additionally, all the nations will recognize my virtue, and via me recognize the true creed and Emunah, and discard their idols. This is wrapping me with a Me'il over all the garments and the salvation. All will see it (that He is Elokai due to my virtue - Tagel Nafshi bEi'lokai), and it is not sewn to my size. The Tzedakah is revealed so all Nochrim will recognize Emunah in Hashem.
Malbim: For this, Sos Asis ba'Shem.
What is the comparison to a Chasan?
Rashi: He wears glorious garments, like a Kohen Gadol.
Radak citing Targum Yonasan: [I will be dressed] like a Chasan in his wedding canopy.
Malbim: The salvation will be the garment that I receive for a gift. Hashem will be like a Chasan who gives beautiful garments to the Kalah for a gift.
Why does it say "Yechahen Pe'er"?
Radak: His glory will be raised via beautiful garments. The Kohen who serves Hashem is the head of the nation and grandeur. Therefore, grandeur is expressed in an expression of Kehunah. The same applies to "u'Vnei David Kohanim Hayu" (Shmuel II, 8:18).
Radak citing Targum Yonasan: [I will be dressed] like a Kohen Gadol in his garments.
Malbim: Refer to 61:10:4:3.
What are a Kalah's Kelim?
Rashi: Her ornaments [Radak - and ribbons].
Malbim: The Me'il will be mine, due to my deeds and virtue. I will be like a Kalah who makes her own ornaments in addition to what the Chasan gave to her.