All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First, all perfect praise be to Allaah who guided you to Islam and we ask Him to increase your religious knowledge and make you steadfast on His religion until you die. The Prophet said: "When Allaah wills good for a person, He enriches him with knowledge." [Al-Bukhari and Muslim]
As regards whether or not a woman should place her arms and palms on the ground when prostrating, then the answerer is that no scholars ruled this as being mandatory. Rather, the majority of them
are of the view that it is desirable for her to stick her belly to her thighs, and her elbows to the side of her body, and place her arms and palms on the floor, and lower her back and buttocks and not raise them as men.
Their evidence is that the general rules of the Islamic Law state that a woman should cover and conceal herself as much as possible. The above-described way of praying is as much as she can do in this regard. However, they do not consider this as being obligatory but only desirable. Their second evidence is the narration you mentioned in the question that the Prophet passed by two women… [Abu Daawood] This is a weak narration.
Nonetheless, other scholars are of the view that the woman should pray like the man prays because of the general evidences which state that a woman is like a man concerning Islamic rulings, especially that the Prophet
said: "Pray in the same manner as you see me praying." [Al-Bukhari] This narration is general for men and women, and there is no evidence for exempting women from this narration. It is confirmed that Um Ad-Dardaa'
used to sit [in Tashahhud] exactly like men sit, so this is evidence that the prayer for women is exactly like the prayer for men. We consider that this view is much closer to the truth.
Allaah knows best.