The arm is not literally a toilet plunger in universe. Firstly, Dalek technology generally had circular controls which let the "plunger" could interact with easily. The arm could also alter its form slightly to better interact with specific objects, for example, finding the combination of electronically-locked doors (Dalek), as well as serving as a weapon.
Doctor Who has shown it suffocating and killing a human by being placed over the nose and mouth, the arm could generate suction to suffocate and kill a human or provide enough force to crush skulls or rip through metal (Dalek and I am a Dalek short story). The Tenth Doctor claimed to have seen one crush a brick with ease (Prisoner of the Daleks novelization). The arm could also scan brainwaves for information or act as a quick intelligence scan (Doomsday, Daleks in Manhattan).