What purpose does a flagellum serve for unicellular organisms? '

The primary purpose that flagellum serves to play in unicellular organisms is that it is used for the process of moving, locomotion. It enables the bacteria or any other single celled being to move with an intended direction across the solution or aqueous environment that it is found in.

It might. it might because if you think about if they discovered if we came from (lets say something funny like aliens) and thy found cells that matched and they would have t do more research about it but would most probably change their theory.