A part, a bit, a portion or a slice.
You would call it a permit or authorization document.
This isn't a matter for speculation. Call your doctor.
A small piece or part of something like a piece of glass is called a shard.
A mouster piece
A piece of chain is called a "link".
A small piece or part of something is called a portion of whatever the thing is.
a slice
A note.
A small piece of something, like chocolate, could be referred to as a "bite" or a "morsel."
A piece of an edge of a circle is called an ARC.
A long piece of clothing is called a "Robe".
The opposite concept of a piece (of something) would be the whole.