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Women counting Sefiras Haomer:
Women are exempt from the Mitzvah of Sefiras HaOmer. [Likewise, based on Kabala, women are not able to fulfill this Mitzvah.] However in certain provinces women have accepted this Mitzvah upon themselves as a complete obligation. [In such provinces, the women are obligated to count due to this custom.] [Practically, the Chabad custom is for women to recite Sefiras HaOmer. Likewise, due to other reasons, all women should recite Sefiras Haomer in the beginning of the night even if they have missed a day and can no longer say a blessing, as it is possible that they must refrain from work throughout the entire night until they do so. The husbands should remind their wives to recite the Sefira each night.]
Women are to count Sefiras Haomer each night, in the beginning of the night, and are to be reminded by their husbands to do so. This applies even if they already missed a day. If they have not missed a day, they may count at night with a blessing.
May women eat prior to counting Sefirah?
Those women who have not accepted upon themselves the Mitzvah of counting Sefirah as an obligation, are not required to abstain from eating beforehand. However, those women who have accepted this Mitzvah upon themselves as an obligation are to follow the same law as men.
A man/child hearing the blessing or count from a woman:
Ø If a man has missed a night, can he be Yotzei the blessing from another woman, such as his wife or daughter?
Ø If a man overheard the blessing/counting from a woman, may he still count with a blessing?
A man, including a male child, who overheard a woman say the blessing/Sefira does not fulfill his obligation according to any opinion and is thus to repeat the Sefira with a blessing. Thus, if man has missed a night, he cannot be Yotzei the blessing from another woman, and is rather to hear it from another man.
If a woman overheard the blessing/counting from another woman, may she still count with a blessing?
No. She may no longer count with a blessing unless she explicitly had in mind to not be Yotzei the count she overheard, prior to overhearing it.
 Admur 489:2; M”A 489:1; See Piskeiy Teshuvos 489:7; Nitei Gavriel Pesach Vol. 3 24:1-4
 Admur ibid; M”A ibid; Rambam Temidim Umusafim 7:24 “Women are exempt from it”; Chinuch Mitzvah 306; See Nitei Gavriel Pesach Vol. 3 24:1 footnote 1 in length
The reason: As this Mitzvah is a time dependent command, of which women are exempt. [Admur ibid] This is learned from the verse “Lemaan Tihiyeh Toras Hashem Bificha” that is written regarding Tefillin which teaches that the entire Torah is connected to the Mitzvah of Tefillin. Now just like women and slaves are exempt from wearing Tefillin, due to the reason explained in 38:3, and Tefillin is a time dependent Mitzvah, as the Mitzvah of Tefillin does not apply on Shabbos and Yom Tov, so too from here we learn that all time dependent Mitzvos women and slaves are exempt from, with exception to some specific Mitzvos. [Admur 17:1; Levush 17:2]
Other opinions: Some Poskim hold that the Mitzvah of Sefiras Haomer is not considered a time dependent command, and women are hence obligated in the Mitzvah. [Ramban Kiddushin 34a “The Tana omitted many Mitzvos that women are obligated in, including….Sefiras Hamoer”; Maharam Chalvaah in Shitas Hakadmonim Bava Kama p. 334; See Avnei Nezer 384; See Divrei Malkiel 3:5 that this is a misprint in Ramban] The reason for this is because the Mitzvah is dependent on the Omer sacrifice and not on a specific time. [Maharam Chalvaah ibid; Kinyan Torah 4:44 based on Turei Even Megillah 20b] Alternatively, it is because women are obligated in Matzah and Chametz, and are hence also obligated in the Mitzvah of Sefiras Haomer, which begins during Pesach. [Avnei Nezer ibid] See also Mikraeiy Kodesh 2:67 and Piskeiy Teshuvos ibid
 M”A ibid based on Zohar Tetzaveh and Emor p. 97b “The 50 days are days of the male world, and are given only to men”; brought also in Birkeiy Yosef 489:22; Daas Torah 489:1; Avnei Nezer 384; Kaf Hachaim 489:9; Rav Poalim 1:12 based on Kabbalah
 So writes Admur ibid; However see M”A ibid who writes “Although women are exempt, the women have already accepted the Mitzvah upon themselves as an obligation.” He does not distinguish between provinces, and certainly does not limit it to certain provinces as writes Admur ibid. The M”B 489:3 writes that in these provinces women are not accustomed to count Sefira at all. In the home of the Steplier women would count Sefiras Haomer. [Orchos Rabbeinu 2:92]
 Admur ibid; M”A ibid; Chok Yaakov 489:3; Elya Raba 489:2; Aruch Hashulchan 489:4; Mishnas Sachir 134; See Nitei Gavriel Pesach Vol. 3 24:1 footnote 3 in length
Other opinions: Some Poskim question the above ruling, stating that there is no source for saying that women accepted this Mitzvah upon themselves as an obligation. [Minchas Chinuch Mitzvah 306; See M”B ibid]
 See regarding Shofar and Lulav: Admur 17:3; Shut Rav Akiva Eiger 1 Hashmatos; Ashel Avraham Butchach 689 and Mahadurah Tinyana 592
 Hiskashrus; Otzer Minhagei Chabad Nissan p. 254
 See Admur 493:9; brought in Halacha 5!
 See Piskeiy Teshuvos ibid footnote 35; Nitei Gavriel Pesach Vol. 3 24:3
 Admur ibid; Aruch Hashulchan 489:4; See Nitei Gavriel Pesach Vol. 3 24:3 that if she has a reminder, such as a calendar, then she may say a blessing even according to the Shulchan Shlomo brought next in other opinions; So rule regarding all Mitzvos that women are exempt: Admur 589:2; 17:3; Rama 589:6; Taz 658:9; M”A 658:11; M”B 655:1; Rabbeinu Tam R”H 33a; Ran; Rosh in name of Mahritz Geios; Tur 589; Ritva Sukkah 2; Rashba 123; Maggid Mishneh Shofar 2 in name of Rashba; Shut Min Hashamayim 1; Birkeiy Yosef 654:2; Yosef Ometz 82; See Kaf Hachaim 17:4; 589:23
Other opinions regarding Sefiras Haomer: Some Poskim rule that women are not to count Sefira with a blessing. [Shulchan Shlomo 489, brought in M”B 489:3; Kaf Hachaim 489:9; Minchas Haomer 10] The reason for this is because they will most certainly miss a certain night and hence even initially we know their counting will be incomplete. [Shulchan Shlomo ibid; M”B ibid; Kaf Hachaim ibid] To note however that according to the Rebbe’s explanation of the dispute in 489:23 that in truth all agree that each day is a separate Mitzvah, and missing a day only holds the future days in question, there is no worry whatsoever if the women miss a future day as it has no affect, according to any opinion on the previous Mitzvos fulfilled. [See Likkutei Sichos 1:270]
Other opinions and Sephardi custom regarding all Mitzvos that women are exempt: According to the Sephardic custom, women are not to say the blessing upon counting Sefiras Haomer. [Kaf Hachaim ibid; Nitei Gavriel 24:2] In addition to the above-mentioned issue, some Poskim rule that women may never recite a blessing over any Mitzvah that they are not obligated in. [Michaber 589:6; Beis Yosef 589; Rambam Hilchos Tzitzis; Igur in name of Reb Yeshaya; Rashi, brought in Hagahos on Rambam; Chacham Tzevi; Yabia Omer 1:39-40] The Michaber ibid rules that they cannot say a blessing as Safek Brachos Lihakel. [Beis Yosef 589] The Birkeiy Yosef ibid states that after seeing the answer from heaven in Shut Min Hashamayim he retracted his ruling like the Michaber and would tell women to recite a blessing. He concludes that if the Michaber would have seen the Shut Min Hashamayim certainly he too would have retracted his ruling.
 The reason: There is no worry of prohibition involved for women to recite a blessing on Sefiras Haomer despite the fact that they are exempt, as explained in 17:3. [Admur ibid] The reason for this is because men are commanded in this Mitzvah and when a woman performs a command that she is exempt from fulfilling, although she is not rewarded as much as one who was commanded, nevertheless she does receive some reward. For this reason, they are permitted to recite a blessing over all the Mitzvos that they are exempt from, if the Mitzvah is performed properly, in a way that a man would fulfill his obligation. [Admur 17:3]
 See regarding Shofar: Ashel Avraham Butchach 689 and Mahadurah Tinyana 592
 P”M 489 A”A 1; Nitei Gavriel Pesach Vol. 3 24:4
 As one can only be Yotzei with another “If he heard from one who is obligated in this Mitzvah” [Admur 489:1] and a woman is not obligated in Sefiras Haomer [Admur 489:2] while a man is obligated in the Mitzvah either Biblically or Rabbinically. Furthermore, even a male child who has reached the age of Chinuch, cannot be Yotzei with a woman being that she is not obligated at all, while he is obligated due to Chinuch. [Nitei Gavriel ibid]
 So seems Pashut, being that both women are of the same level of obligation [i.e. exempt] and hence one can be Motzi the other, as explained in previous footnote. However, Tzaruch Iyun, as a) Some Poskim rule women are not included in Areivus and hence cannot be Motzi, [See Rosh and Rabbeinu Yona Barchos 20b; P”M 271 A”A 2; 689 A”A 4; Degul Merivava 271 and Tzlach Brachos 20b] and b) Perhaps since there is no Mitzvah involved at all for her to say it, she is never considered to be Yotzei with another unless she explicitly has in mind to fulfill it. Vetzaruch Iyun. Nonetheless, due to the doubt that perhaps she is nevertheless Yotzei, certainly she may not repeat the blessing.