copying the selection onto a new layer and deleting the old layer.

This explanation makes no sense. Not sure why. Perhaps you are using the wrong names for things? That is why you are getting very random answer; people don't understand what you mean.

• To deselect (remove/delete a selection) you go to Select > Deselect, or click somewhere outside the selection with a selection tool, or press cmd/ctrl-d.
• To delete the contents of a selection on a raster layer, press the delete key. But usually it is a lot better to turn the selection into a layer mask (click the layer mask button in the layers panel).
• Selections are not stored as layers, or on layers. They can be stored as channels though if you try to save them. You can delete such a channel by dragging it to the trash in the channels panel.
• Quick Mask (Q) let's you visualize a selection as a red overlay on your image. You can then e.g. paint with the brush tool to add/remove from the selection. Once done press Q again and the red overlay you created gets converted back to a regular selection and you can continue working.