Short answers, pulled from the story.
Faith in Buddhism is defined as a serene commitment to practice rather than blind belief. It represents trust and surrender to enlightened beings such as Buddhas or bodhisattvas who aim to become fully awakened.
During the reign of Emperor Ashoka around 250 BCE Buddhists placed greater emphasis on faith to unify his empire. This period saw increased worship of Avadana literature and new devotionalism known as bhakti emerging across Indian religion.
Honen born 1133 died 1212 and his student Shinran born 1173 died 1262 developed new Japanese Pure Land schools drawing on earlier Chinese masters Tanluan and Shandao. They taught that mindfully reciting the nembutsu phrase would secure entrance into Amitabha's Pure Land for ordinary people.
White Lotus sectarianism arose in China during fourteenth century encompassing beliefs about coming Maitreya Buddha during apocalyptic age. Devotees believed correct teachings would save them when new world era arrived persisting into nineteenth century when Chinese associated Maitreya's arrival with political revolution.
Western intellectuals during eighteenth century Enlightenment began viewing religion culturally relative opposing single truth discernible through reason alone. By end nineteenth century western writers like Edwin Arnold presented Buddhism rational unburdened culture answering contradiction science versus religion.