There's no sign of what the piece from the first segment of the dance is called, but it strongly resembles - it's even in the same key - Coelacanth, from the 1985 album Oil and Gold by the British alternative rock band Shriekback. I've no idea if the Young Dancer piece, which features ethnic vocals, is a cover, a homage, coincidence, or what. For comparison:
Movie enthusiasts will recognise Coelacanth as the track behind a classic segment of the 1986 Manhunter - the first film version, directed by Michael Mann, of Thomas Harris's novel Red Dragon. This is the powerful scene in which the serial murderer Francis Dolarhyde takes the blind photographic bureau employee Reba McClane to a zoo's veterinary surgery to explore with her hands a tiger anaesthetised for dental treatment. It's a defining scene of the film, in which Dolarhyde - temporarily freed by Reba's blindness from the visually-related triggers to his insanity - shows his human side in an astoundingly creative and sensitive gift. This makes it also a defining moment of the portrayal of Dolarhyde as a great tragic figure.
I've always rated Manhunter highly as a film, and I still think it's much superior in style and atmosphere to the 2002 remake, Red Dragon. As to Dolarhyde in the latter, Ralph Fiennes is an excellent actor, but he portrays Dolarhyde with a lack of affect, unlike Tom Noonan in the original, who leaves us in no doubt, in the tiger scene and the one where Reba spends the night with him, what a tortured character Dolarhyde is. According to Wikipedia, Manhunter's director Michael Mann was a fan of Shriekback, and this accounts for three of the band's tracks appearing in the film: Coelacanth, This Big Hush, and Evaporation. It's further backed with tracks by other rock bands not well-known: The Prime Movers, Red 7, The Reds, and Iron Butterfly. It was a film made with the courage to be distinctive.
A commenter to the tiger video, Pristine S., suggests that the scene is "an extraordinary literary hat tip" to the blind writer Jorge Luis Borges, who recalled seeing a tiger as one of his early visual memories. It may or may not be intentional, and it's not in the book. Unlike Borges, Reba has never seen a tiger:
"Did you ever look at a tiger?"But it's a nice literary connection nonetheless.
She was glad he could ask the question. "No. I remember a puma when I was little. That's all they had at the zoo in Red Door. I think we better talk about this."
- Thomas Harris, Red Dragon, 1981
The tiger I remember was one of the first things I saw in my life. I remember that I was going to the zoo. that I didn't see other animals … I felt drawn to tigers, those first things I saw in life. Later came years of myopia, years of blindness, but there was one color that survived. It was the color yellow. And that's why I entitled a book. The Gold of the Tigers.
- Jorge Luis Borges: Conversations, Jorge Luis Borges, ed. Richard Burgin, Univ. Press of Mississippi, 1998