Short answers, pulled from the story.
Bodhipakkhiyādhammā is a Pali term meaning qualities conducive or related to awakening. It refers to seven sets of mental qualities totaling thirty-seven items that are developed through meditative practice, recognized by both Theravadan and Mahayanan Buddhists as a shared map of the path to bodhi.
The standard Pali tradition lists thirty-seven qualities across seven sets, though the sets are described as repetitious and interrelated. Buddhaghosa, working from Vism. XXII.40-43, reduced these to fourteen non-redundant qualities after removing duplicates.
The seven sets are the four foundations of mindfulness, the four right kinds of striving, the four bases of spiritual power, the five spiritual faculties, the five spiritual powers, the seven factors of enlightenment, and the Noble Eightfold Path.
The Buddha taught the bodhipakkhiya dhammas in several major texts, including the Maha-parinibbana Sutta (DN 16), the Bhāvanānuyutta sutta (AN 7.67), and the Greater Discourse to Sakuludayin (MN 77). The Samyutta Nikaya devotes its first seven chapters of the fifth division to these sets, containing close to nine hundred discourses.
Yes. Versions of the lists appear in the agamas of other early Buddhist schools. The Dharmaguptaka school's version, preserved in Chinese translations of the Dirghagama and the Dharmaguptaka vinaya, lists forty-one qualities rather than thirty-seven, including the rupa jhanas that the Pali tradition omits.
Buddhaghosa addressed the bodhipakkhiya dhammas extensively in the Visuddhimagga at sections XXII.33-43. He enumerated all seven sets, described each one, analyzed how they exist in the consciousness of an arahant, and identified fourteen non-redundant qualities by removing the five qualities that recur across multiple sets: faith, energy, mindfulness, concentration, and wisdom.