operator overloading error

Solution is simple :

not all code path return value

You don't return anything in your method.

Look at the signature of the method :

public static vector operator +(vector v1, vector v2)

You have to return a vector from the method. Thus :

public static vector operator +(vector v1, vector v2)
{
   return new vector(v1.X * v2.Y + v2.X * v1.Y, v1.Y * v2.Y);
}

I suggest you get a good book on C# basis ; this is a fundamental field here that you seem to ignore.

Good luck.