Hi,
Just to clarify, you want to work with an individual part in a specific layer without modifying any other overlapping part from other layers, correct? You mentioned that even though you dont have those other layers showing, you still select the parts in them that overlap with your own. I'm assuming this has to do with the fact that you have only hidden the other layers, not disabled them. In your left design toolbox section, double click on the layer you want to work with and then click on the boxes next to the layers you want to avoid until the boxes are white and empty. This way, you disable them and can comfortably work on the one active layer. You can always reenable them after you're done working on one part. Let me know if this helped.
Kind Regards,
Miguel V
National Instruments