1. The Rama (O.C. 610:4) writes that the minhag is to wear white on Y"K to appear like an angel, which is also why we wear a kittil. Additionally, the kittil is a reminder of shrouds, which reminds a person of death and causes a person to have humility and be contrite.
The MG"A comments on this Rama that the Midrash indicates that angels are male (my wife commented that an angel can't reproduce, so gender doesn't have much meaning up there. I assume the terms male/female in this context are meant in the sense of mashpia vs. mekabeil, or chomer vs tzurah, though I found that the Anaf Yosef on the Midrash Rabbah, Vayikra 31:5 asks this question and gives a different answer), and therefore women need not wear white. However, they may wear a kittil to remind them of death. Women, according to the MG"A, are not angels.
The M"B quotes the Mateh Ephraim who holds exactly the opposite. Women should also wear white, but the custom is for women to not wear a kittil. Interestingly, though, in O.C. 619:5 when the S.A. quotes the din of standing for all of davening, which is based on the idea of trying to be like an angel (they stand around on their one foot all day), the M.B. in the Sha'ar haTziyun writes that this does not apply to women. The source is the previous din in O.C. 610, which seems true only if you hold like the MG"A. To make matters more confusing, the reason the Tur gives for our saying "Baruch Shem K'vod Malchuso..." out loud is because Moshe heard the angels reciting this phrase, and on Yom Kippur we want to be like angels. As far as I know, women also recite the phrase out loud as well.
2. Erev Y"K I was trying to find my kittil when my daughter reminded me that at the seder I had not worn a kittil since I am unfortunately in aveilus this year for my father. Lichorah, the same logic should apply to Y"K as well. She is absolutely right. The Taz understands that the Rama is giving two reasons for wearing a kittil: 1) to be angelic; 2) to remind one of the yom ha'misah. On Pesach as well, like reason #1 here, there are many positive uplifting reasons to wear a kittil, many of which are summarized in this post by R' Eliezer Eisenberg, who already has a full treatment of this topic to which I can add very little. If the reason for wearing a kittil is a reminder of death, then there is no reason an aveil cannot wear one (though the MG"A in Hil Pesach writes that an aveil need not wear one since he has death on his mind without it); if the reason is to have some more positive experience of Yom Tov or of simcha, than the aveil is excluded because he is not supposed to be having positive uplifting experiences during aveilus. The Aruch haShulchan and R' Moshe both opine that an aveil should not wear a kittil on Y"K. What I found interesting in that in Hil Pesach, the M"B (472 s"k 13) first writes that an aveil should not wear the kittil, but if he does, one need not object because the Taz says it is permitted. In Hil Y"K (610 s"k 17) the M"B first quotes (giving this view primacy) the Taz's view that an aveil may wear a kittil and then quotes that there are minhagim not to. Why give the Taz primacy here but put it on the back burner in Hil Pesach?
3. The poskim have problems with the line in Ne'ilah, "Hayom yifneh, hashemesh yavo..." If it is already after shekiya (which it was where I was davening when the shat"z got to this line, and I think that is probably true of many of not most places), then the day has in fact passed and the sun is down already, so the future tense seems wrong. I saw that R' Chaim Kanievkey said to chang the nusach to past tense (i.e. "hayom panah, hashemesh ba'ah...") though the Aruch haShulchan opines that one need not do so. In any case, it seems strange to me that in the previous line we say, "Psach lanu sha'ar... ki panah yom," here using the past tense. Is it "panah yom" or "yifneh yom?" I don't know how you can have it both ways.
4. Nu, on to preparing for Sukkos. The Shem m'Shmuel writes that the reason we do na'anuim by waving the lulav away from and then to the heart is because while on Y"K we got our mind in order and now understand mentally what we need to do with out lives, we need to bring the lesson into our hearts, and that's what Sukkos is for.