Does Islam tell us to recite al-Faatihah one hundred times when asking Allaah for something?

There is no saheeh evidence (daleel) to indicate that we should recite al-Faatihah one hundred times when asking Allah for anything, so it is not permissible to do this. You must follow the Sunnah and call on Allah by His names and attributes, as he says (interpretation of the meaning): “And (all) the Most beautiful Names belong to Allah, so call on Him by them…” [al-A’raaf 7:180]. As regards Soorat al-Faatihah, it is the greatest soorah of the Quran, so recite it whenever you wish, without specifying a certain number of times or a certain way of reciting it that has no basis in Islam.

May Allah help us and you to do all good.