Do aeroplanes have to balance torque like helicopters? Helicopters need a tail rotor to balance the torque reaction that tends to rotate the main body sideways. Doesnt a single-engine plane suffer the same problem? I would imagine that (for example) the left wing would dip lower than the right due to the torque. How is it countered?
A single engine plane can suffer from control problems due to torque.

An early famous example was the Sopwith Camel

As others have pointed out, torque effects have to be countered using the normal aerodynamic controls available to the pilot. Some aircraft had extra-large ailerons because of this issue.