Praise be to Allah.
The correct view is that there is no difference between a woman’s prayer and a man’s prayer. There is no evidence for what some of the jurists have mentioned about the differences. The hadith which you quoted in your question, which is the words of the Prophet (blessings and peace of Allah be upon him): “Pray as you have seen me praying,” includes everyone, and Islamic rulings apply to both men and women, unless there is evidence to indicate that some ruling is specific to one gender and not the other. The Sunnah is for a woman to pray as a man prays in terms of bowing, prostration and recitation. Putting the hands on the chest is what is best, and the same applies to putting the hands on the knees when bowing, and putting them on the ground when prostrating in line with the shoulders or in line with the ears, and the same applies to making the back straight when bowing, and the same applies to what is to be said when bowing and prostrating, after rising from bowing and after rising from the first prostration. In all of that, women should do the same as men, in accordance with the words of the Prophet (blessings and peace of Allah be upon him): “Pray as you have seen me praying.” Narrated by al-Bukhari in as-Sahih.
With regard to the iqamah and adhan, they are something separate from the prayer. The iqamah and adhan are for men only, as is stated in the religious texts. It is men who give the iqamah and adhan; the case of women, there is no iqamah and no adhan. With regard to reciting out loud, a woman may recite out loud in Fajr, Maghrib and ‘Isha’. In Fajr she may recite out loud in both rak‘ahs; in Maghrib she may recite out loud in the first two rak‘ahs; and in ‘Isha’ she may recite out loud in the first two rak‘ahs, just as men may do. End quote.
Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him).
Fatawa Nur ‘ala ad-Darb (2/799).