if someone (a woman) stays up all night and only goes to sleep once it is completely morning, which tefillos are they allowed to daven?
A woman who is up all night basically davens the same Tefilla she normally davens. The questions arise in regard to certain birkot Hashachar. In regard to the Bracha on Netilat Yadayim, before washing her hands she should use the bathroom and then she would be able to say the Bracha. (Mishna Brura 4:30) However, the sefardi custom is not to say the Bracha. In regard to Birkot Hatorah (La'asok b'divrei tora, Hamelamed torah l'amoYisrael, Asher Bachar Banu) there is a dispute if upon a new day they must be said again even for men who haven't slept . Therefore the custom among men is, that because of the doubt the best would be to hear the bracha from somebody who is definitely required and then say some psukim in order to fulfill the Mitzva of learning Torah. Alternatively, when "Ahava Rabba" or "Ahavat olam" is said before Kriat Shema they should have in mind that it is taking place for Birkat Hatorah and then learn Torah after Davening.(Mishna Brura 47: 28) In regard to women, the general tendency when there is a doubt in regard to Birkot Hatorah to exempt them. (Kaf Hachaim 46: 34). Therefore, it would seem that women who are uop all night should be exempt because of the doubt. However, in the Hebrew counterpart of this website, Rabbi Eliezer Melamed suggests that a woman in such a case should say Ahava Rabba" or "Ahavat olam" before Kriat Shema and this would be in place of their Birkat Hatorah and then she should recite Kriat Shema which would then be considered as Torah study. There is also a question about saying "Elokay Neshama" and Ham'avir shena etc." In this case she should preferably hear from someone else who has slept and if that is not possible, then she may say them herself. In short, the question of what is to be said applies only to certain berachot but not the entire Tefilla. 1. Netliat Yadyim, the bracha should be after having used the bathroom. 2. Birkat Hatorah should preferably be heard from someone else who has slept and if that is not possible she should Ahava Rabba before kiriat shema instead of Birkot Hatorah. 3. Elokay Neshama and Hamavir Shena should also preferably be heard from someone else who has slept and if that is not possible they may be said by the person who has not slept.