1)The obligation of Megilah for women is different than the obligation for men, in that women are only obligated to "hear" the Megilah, whereas men are obligated to "read" the Megilah.
In fact, according to many Poskim, when a man reads the Megilah for a woman, or if a woman reads the Megilah herself, the Bracha she recites is not "Boruch Ata Hashem...Al Mikra Megilah- on the reading of the Megilah" rather she says "Boruch Ata...LiShmoa Mikra Megila- on the hearing of the reading of Megilah" (Ram"a Siman 689:2 and Mishna Berura ibid.:8. This is also the opinion of the Chayei Adam. However, the opinion of the Gaon of Vilna (in Ma'aseh Rav) as well as the Pri Chadash 689:2 and others is that even women make "Al Mikra Megila")
Being that the obligation of women is not the same as men, a woman may not read the Megila for men.
She may, however, read the Megilah for another woman. (Mishna Berura ibid: 7). However, according to some Poskim, a woman may not read the Megilah for an entire group of women. (Sha'ar Hatzion ibid.)
All of the above is B'dieved, as ideally (L'Chatchilah) a woman should not read the Megila herself, rather she should hear it from a man, if at all possible. (Mogen Avraham quoted in Mishna Berura ibid. 8)
2) All the Halachos of reading the Megila (many of which we will iy"H learn in the near future) that apply to men, apply to women as well. Therefore, a woman who went to Shul to hear the Megilah but could not hear clearly, and missed a few [or more] words, should hear it again when she gets home [from a man reading from a kosher Megilah].
Alternatively, if the women possesses a kosher Megila, she should bring it to Shul and quietly read along as the Ba'al Koreh is reading, thus ensuring that she doesn't miss even one word. (Pri Megadim- Aishel Avraham Siman 689:11.)
However, one (man or woman) that does not have a kosher Megilah, and is following along in a printed Megilah, should not read along with the Ba'al Koreh. (Chayei Adam Klal 155:17)
Important Numbers
