Short answers, pulled from the story.
Buddhist prostration is the practice of bowing the body fully to the ground as an act of reverence toward the Triple Gem: the Buddha, the Dhamma, and the Sangha. The Pali term is panipata; the Sanskrit equivalent is namaskar. The practice is understood to purify defilements, accumulate merit, and give an experience of veneration.
In the five-point veneration, known in Pali as patitthitapanca or pañc'anga-vandana, the practitioner places both forearms from palm to elbow on the floor, with the elbows touching the knees and the hands palm-down roughly four to six inches apart. The forehead rests between the hands and the knees remain about a foot apart.
In Thailand, each of the three daily prostrations is paired with a Pali verse. The first bow includes "Araham samma-sambuddho bhagava, Buddham bhagavantam abhivademi," saluting the Buddha as the Noble, fully Enlightened One. Separate verses honor the Dhamma using "Svakkhato bhagavata dhammo" and the Sangha using "Supatipanno bhagavato savakasangho."
"Horizontalizing the mast of ego" is Roshi Philip Kapleau's phrase for what full prostration accomplishes. He describes the act as cleansing the heart-mind and rendering it flexible and expansive, made possible under the impetus of reverence and gratitude.
The lotus bud mudra is a hand gesture in which the base of the palm and the fingertips touch with the thumbs slightly tucked. In Vajrayana prostration, the practitioner places this gesture at the crown, throat, and heart in sequence, offering homage to Guru Rinpoche's enlightened body, speech, and mind respectively.
In Vajrayana ngöndro, a set of preliminary practices preparing the student for tantra, prostrations are typically performed one hundred thousand times. Other components of the ngöndro sequence include recitations of the Refuge prayer, mandala offerings, and Vajrasattva mantras.