Short answers, pulled from the story.
In Buddhism, faith (saddha in Pali, sraddha in Sanskrit) refers to a serene commitment to the practice of the Buddha's teaching and trust in enlightened beings such as Buddhas or bodhisattvas. It is not blind belief but a quality that is meant to be deepened through personal verification of spiritual truth, progressing from initial trust toward wisdom.
The Triple Gem consists of the Buddha, the dharma (his teaching), and the sangha (the community of spiritually developed followers). Faith in early Buddhism oriented itself toward these three, expressed through the act of taking refuge by reciting a short verbal formula naming each.
In Pure Land Buddhism, faith in the compassionate power of the Buddha Amitabha is the central practice. The Japanese teacher Shinran (1173-1262) taught that a single sincere recitation of Amitabha's name was sufficient for birth in the Pure Land, and that this faith (shinjin) was itself a gift granted by Amitabha rather than something the practitioner could build up through effort.
Nichiren (1222-82) was a Japanese Buddhist teacher who taught that faith in and worship of the Lotus Sutra, specifically the chanting of its title, was the only effective practice for his age. He believed that devotion to the Lotus Sutra would allow practitioners to unite with a primordial Buddha, and he criticized all other schools of Buddhism sharply. Today more than forty organizations continue the Nichiren tradition.
From the nineteenth century onward, Buddhist modernism in countries such as Sri Lanka and Japan downplayed and criticized devotional faith, presenting Buddhism as a rational philosophy aligned with science. In Sri Lanka, British-educated intellectuals promoted what scholars call protestant Buddhism, stripping away relic worship and devotional practice. From the 1980s onward, scholars observed this influence weakening as devotional religiosity resurged.
In the Kalama Sutta, the Buddha argues against following sacred authority, tradition, or logic, and against respecting teachers for the mere fact that they are teachers. Instead, practitioners should verify teachings through personal experience, distinguishing what leads to happiness and benefit from what does not. Buddhist translator Bhikkhu Bodhi has argued that many modern interpreters misread this sutta as dismissing faith, when the Buddha taught that faith and personal verification should go hand-in-hand.