You asked “when does davening for 9 hrs, come before learning torah?”
Ever heard of Yom Kippur? The holiest day of the year. Davening in most shuls on Yom Kippur is longer than 9 hours and people on higher levels spend their entire Yom Kippur in the Bais medrash begging Hashem for teshuva. They sit and say tehillim between musaf and Mincha and never leave the Bais medrash begging Hashem forgiveness.