The Cherry.
They are actually called cigarette butts, and they are the white part on the end of a cigarette, hence the name butt.
If the 'part' is a role for an actor, the term is 'bit part'. If the 'part' is a snippet of film, it may be called a scene or part of a scene.
A stale cigarette. A stale cigarette has no taste whatsoever.
Cigarette Pack Collector.
Small leftover pieces of cigarette are called cigarette butts.
No part that I know of.
the butt or the filter
Small leftover pieces of cigarette are called cigarette butts.
A 'stub'.
A tobacconist.
A short.