Yes, the 2-stroke oil is for premixing with gasoline.
Use "regular" motor oil for the engine...
I recommend 15W40 (usually labelled for "diesel engines," but it's good for your engine due to added detergents) or 20W50.
The higher weight oils are good for your rotary since the thicker oil is better for protection.
Most of us do not worry about gas mileage...
-Ted