All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Thank you for your great desire to do good for the sake of pleasing Allah. It is the duty of each and every Muslim to endeavor to please Allah and perform the prayer at its prescribed fixed time. It is narrated in a sound Hadeeth that the Prophet Muhammad was asked: “Which deed is most beloved to Allah? He said: “To perform the prayer at its prescribed fixed time”. Then the questioner asked: “And then?” The Prophet Muhammad replied: “Obeying one's parents”. The questioner again asked: “And then?” The Prophet Muhammad replied: “Jihad for the sake of Allah.” [Bukhari and Muslim]
Know –may Allah guide you to the right path –that performing the prayer at its prescribed fixed times is an obligation on all Muslims, men and women alike. The Prophet Muhammad said: “Women are the second half of men.” [Abu Dawood and At-Tirmithi]
The Prophet Muhammad also said:
“I have been given five (things) which were not given to anyone else before me: 1. Allah made me victorious by awe, (by His frightening my enemies) for a distance of one month's journey. 2. The earth has been made for me (and for my followers) a place for offering the prayer and a thing to purify (perform Tayammum); therefore anyone of my followers can offer the prayer wherever he is, at the time of the prayer. 3. The booty has been made lawful to me, yet it was not lawful to anyone else before me. 4. I have been given the right of intercession (on the Day of Resurrection). 5. Every Prophet used to be sent to his nation only but I have been sent to all mankind.” [Al-Bukhari and Muslim]
The Scholars state that what is meant is not only the men but also the women, but using “man” for both is preponderant in the Arabic language. The Prophet Muhammad made clear that whenever the time of the prayer comes, one should pray wherever they are. If the Muslim women are fearful of missing the prayer on time by waiting till they go home, they should pray wherever they are. Allah Says (what means): {Indeed, prayer has been decreed upon the believers a decree of specified times.} [Quran 4:103]
You should know –may Allah guide you to the right path –that there is no harm for women to pray in public places in front of others if they are covering themselves. It may even be a sort of calling non-Muslims to embrace Islam.
If non-Muslims see these movements which Muslims do and the different states of Sujood (prostration), Rukoo’ (bowing down), and Khushoo’ (submissiveness and attentiveness), they might be influenced and try to learn the religion and the wisdom behind these movements. This might lead them to reading the Quran or some of its translations. Allah may lead some of them to Islam.
Finally, we ask Allah to guide us all to do what pleases Him and to help us all support the truth.
Allah knows best.