Get coordinates after rotation

Questions
1

I use GPU picking to get hovered object. When i get active object coordinates i translate it to real world using this code:

private _translateCoordinates(x: number, y: number): any {
   const vector = new Vector3(x, y, 0);

   const widthHalf = 0.5 * this._renderer.context.canvas.width;
   const heightHalf = 0.5 * this._renderer.context.canvas.height;

   vector.project(this._camera);

   vector.x = ( vector.x * widthHalf ) + widthHalf;
   vector.y = - ( vector.y * heightHalf ) + heightHalf;

   return {
      x: vector.x,
      y: vector.y
   };
}

But the coordinates are wrong if I rotated the scene. How can I take into account the rotation of the scene when translating the coordinates.
I tried

vector.applyMatrix4(this._scene.matrixWorld)

but it did not give the desired result.

2

I fixed previous code by adding
vector.applyQuaternion(this._scene.quaternion);

But i can’t understand how fix code for object dragging. Here the code:

if (!this._dragInProgress) {
        const worldVector = new Vector3();
        this._camera.getWorldDirection(worldVector);
        this._plane.setFromNormalAndCoplanarPoint(worldVector, new Vector3(this._nodesLayer.hoveredNode.x, this._nodesLayer.hoveredNode.y, 0));
        this._raycaster.setFromCamera(mouse, this._camera);
        this._raycaster.ray.intersectPlane(this._plane, this._intersection);
        this._offset.copy(this._intersection).sub(new Vector3(this._nodesLayer.hoveredNode.x, this._nodesLayer.hoveredNode.y, 0));
        newPos = this._intersection.sub(this._offset).clone();

        this._dragInProgress = true;
      } else {
        this._raycaster.setFromCamera(mouse, this._camera);
        this._raycaster.ray.intersectPlane(this._plane, this._intersection);
        newPos = this._intersection.sub(this._offset).clone();
      }