or other places of great crowding, where worshipers simply cannot avoid walking in front of someone who is praying; in such cases there is no blame, given the hardship and necessity involved.

As for whose passage actually breaks the prayer, the scholars have differed. The correct opinion—preferred by Shaykh Taqi ad-Din, Shaykh al-Islam Ibn Taymiyyah, may Allah have mercy on him, and others—is that the prayer is invalidated by the passage of a dog, a donkey, or a woman. Allah knows best.
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Supplication after the prayer

Question: After finishing my prayer I regularly make the following supplication: “O Allah, accept our prayer, purify our hearts, have mercy on our parents, forgive our deceased, relieve our distress, grant us good, and forgive the believing men and believing women.” I say this every time I complete the prayer. Is it permissible for me to do so? Please advise us, and may Allah reward you with goodness.

Answer: Persistently adhering to this particular supplication and reciting it after every prayer is not prescribed, because, as far as I know, nothing of this sort has been transmitted from the Messenger of Allah ﷺ for that specific occasion. However, if you say it on some occasions without making it a regular practice, there is no harm in that, God willing.
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Reciting al-Fātiḥah after the prayer

Question: Some members of the congregation recite Sūrat al-Fātiḥah after the prayer on the assumption that it is a supplication or a means of blessing. Is this practice in any way part of the Sunnah? They then recite it a second time as a gift to the souls of the deceased. What is the ruling on this?