Yeah they go in the FLA. They don't have to go on the stage, just in the library.
I am not so sure about this, I just went through it with my datagrid component, and I had to drag them to the stage and stick them in guide layers in order for them to get packaged up with my component. When I just had them in the library and I packaged and installed them into a component and then dragged thatonto a new movie the library items never made it. I always had to make sure they were on the stage of my component fla. I have never really figured it out, but as far as I know this is how it had to be done.