What would happen if a multi engine operated symmetrically? So if one engine were to rotate counter-clockwise and the other clockwise. What are the advantages and downsides to this?
A single engine plane yaws to the opposite direction of the engine spinning. This is called the p-factor It's the same with a twin, with both engines rotating into the same direction. Rudder input is needed to fly straight.
When the engines operate symmetrically, this effect cancelles out. The plane is easier to fly.
It's also explained in this video about twins.
An example of a counter-rotating multi-engine plane is the Lockheed P-38 Lightning.
[The P-38] featured two 1,000 hp (746 kW) turbosupercharged 12-cylinder Allison V-1710 engines fitted with counter-rotating propellers to eliminate the effect of engine torque.
Counter-rotation was achieved by the use of "handed" engines, which meant the crankshaft of each engine turned in the opposite direction of its counterpart.
If the engines are turning in the same direction, then if either fails, the net p-factor will not be the same. See: Critical engine.