Short answers, pulled from the story.
Bharatanatyam is an Indian classical dance form from Tamil Nadu, recognized by the Sangeet Natak Akademi as the oldest classical dance tradition in India. It expresses South Indian religious themes, particularly those of Shaivism and Hinduism more broadly.
The Madras Presidency banned temple dancing in 1910, following an anti-dance movement launched in 1892 by Christian missionaries who characterized the tradition as cover for prostitution. The ban was challenged through the Indian independence movement, and Bharatanatyam was revived as a mainstream public art form in the early 20th century, with state-sponsored festivals beginning in 1955.
The Natya Shastra is a Sanskrit treatise attributed to the ancient scholar Bharata, with its first complete compilation dated to between 500 BCE and 200 CE. It defines the theory of Tandava dance, rasa, bhava, gestures, postures, and acting techniques that form the foundation of Bharatanatyam and other Indian classical dance forms. The most studied version contains about 6,000 verses in 36 chapters.
An arangetram is a solo debut performance marking the completion of a dancer's initial formal training. The term translates as "ascending the stage." It typically takes place ten to twelve years after training begins, and the dancer performs solo for approximately three hours; the timing is set by the guru, not by a fixed schedule.
E. Krishna Iyer, a lawyer who studied from traditional Sadir practitioners and was imprisoned for his advocacy, and Rukmini Devi Arundale, who developed the Kalakshetra style, were central to the revival. Balasaraswati, Yamini Krishnamurti, and the American dancer Esther Sherman (who took the name Ragini Devi after moving to India in 1930) also played significant roles.
Margam is the traditional seven to eight-part order of presentation in a Bharatanatyam performance. It moves from the opening Pushpanjali or Alarippu through Jatiswaram, Shabdam, the central Varnam (which can last 30-45 minutes or more), Padam, Tillana, and finally a Shlokam or Mangalam. Balasaraswati described its arc as moving from pure meter to a final non-metrical song, calling it a "most wonderful completeness and symmetry."