Is there an actual mitzvah for women to dress tzanua in and of itself? Or is it simply helping out a man's mitzvah of not looking at ervah when learning/saying brachas, and not being led to forbidden thoughts?
I don't think Daagah is worrying about whether there is a HALACHA of tzniut - there are many - but if there is a MITZVAH of tzniut, a Biblical injunctive. Tzniut vis a vis G-d seems to emanate from Deut. 23:10-15, to not re-join your army troop after a nocturnal emission until after mikvah, and to take a shovel into battle to cover feces. The verse recommends modesty, cleanliness & chastity so that "your camp shall be holy" so that "He not see an unseemly thing ("ervah") in you, and turn away from you." We derive laws like defecating modestly from here. Tzniut vis a vis men (or for men, women) seems to be derived from Leviticus 18:6, "None of you should APPROACH to any that is near of kin to him to uncover their nakedness; I am the Lord!" Since the word for approach, TIKRAVU, has a connotation of coming close in some way, the Rabbis understood that to mean anything that increases the likelihood of inappropriate sexual conduct, e.g., suggestive or unduly attractive clothing, suggestive remarks, spending time together in private, etc. (With men tending to become stimulated visually, modesty for women has often revolved around clothes & make-up.) Early non-Biblical sources, but before the Talmud's "Hair in a woman is ervah" & "The thigh (shok, translated by many as the calf) in a woman is ervah", is the Midrash Rabbah Beraishit that while G-d formed Eve, He repeated, "Tznuah te'hei! Tzenuah te'hei!" (Be modest! Be modest!), yet Woman is still challenged in issues of modesty. Also, the Mishnah in Bava Kamah (Ch. 8) where Rabbi Akiva levies a heavy fine on a man who pulled off a woman's head covering for "boshet", personal embarrassment. Though the man proves that she wasn't so careful about uncovering her own hair, Rabbi Akiva doesn't lower the fine. (Sorry if incomplete, I'm working without books here...)
Yes. The Baal HaTanya wrote in his Shulchan Aruch (2:1) (quoting the Tur) that "one shouldn't act in an immodest manner even not in front of other people ... even if one is is alone in a room at night one must be modest in front of Hashem ... therefore one shouldn't reveal his flesh, even a little".
The Mahadura kamma added that modesty adds to one's feeling of subjugation to Hashem.