Firstly: The Two Salams The ruling of the first salam
The first salam is an integral of prayer. There is no leaving the prayer without it. This is the position of the majority: the Malikis, Shafi`is, and Hanbalis. It is also the position of Scholars, Companions, Followers, and those after them. The ruling of the second salam
Scholars are of two positions regarding the second salam:
The first opinion: the second salam is a meritorious sunnah. This is the position of the Maliki and Shafi`is, and one narration from Ahmad. It is the chosen position of Ibn Hazm and Ibn Qudamah.
The second opinion: the second salam is an obligation  Hanafis hold it to be wajib, as they distinguish between wajib and fard (obligatory). . This is the position of the Hanbalis, one position among Malikis, and a position of some literalists. Ibn Baz and Ibn `Uthaymin chose this view. Turning when giving salams
It is sunnah to turn to the right and left when giving salams such that one’s cheek can be seen (from behind). This is the position of the majority: the Hanafis, Shafi`is, and Hanbalis.
Secondly: How a Woman’s Prayer Differs from that of a Man
There is no difference between the prayer of a woman and a man. This is one position among Malikis, and the choice of Ibn Baz, al-Albani, and Ibn `Uthaymin.