Yes, it is possible. All you have to do is to listen for the drawgExit event and then you can do whatever you want with your dragging. Something like this:
mesh.addEventListener( "exitDrag", exitDragEvent );
private function exitDragEvent( e:Event ):void
// this will force your mesh to remain at y = 10, but will allow it to be dragged on x
e.target.y = 10;
With regards to your second question... I'm not sure what rotation you want to prevent. startDrag() doesn't rotate objects...