Origin and end of jivatma?? Is it created or can the atma divide? what happens to atma in nirvana or moksha, how did it come to be, how can it be eternally fragmented from the supreme? How did the fragmentation occur?
First thing first. Atman or self is not part of the Brahman or supreme consciousness. It is an instance of it.
For example, you might have a piece of white paper. That piece is a part of a larger paper. But the whiteness of that piece is not a part of whiteness, it is an instance of whiteness (See Plato's forms).
In Upanishad and later Vedanta philosophy, they always explicitly mentioned that consciousness is undivided. It cannot be split or fragmented because the imagined fragmentation of consciousness is also to be known by consciousness only. The limitation of consciousness is known by consciousness, and therefore, consciousness is not limited. That is to say, it is unlimited. Vedantins used a metaphor of space inside a jar. Space inside a jar and outside the jar is the same space! Isa Upanishad invocation says - "That is full; this is full. The full comes out of the full. Taking the full from the full the full itself remains. Aum, peace, peace, peace."
Vedanta uses the metaphor of ocean and wave to answer questions like this. As waves are created in the ocean, and at the end, it merges into it, similarly jiva emerges from Brahman and merges into it. In reality, both ocean and wave is nothing but water.
Ref. 1.the essence of Vedanta by Brian Hodgkinson 2.Commentary on the Panchadashi (written by Vidyaranya) by Swami Krishnananda