An, any, exported image is a separate file. To Export means to make a copy of the original file with usually a different File Extension, JPG or TIF instead of the RAW file extension, and at the same time apply the edits you have done to that exported image. LR does not really touch the original images. The edits you do on images in LR are saved to the catalog file or to an XMP sidecar file or in the case of DNG, TIF or JPG the edits are actually stored inside the original file in a special area that does not alter the original image. The only time you can see the edits done by LR is when you are viewing the image Inside LR and or when you export an image. Then the edits get Applied to the Exported image.
So to answer you last question.
If you edit an image and then Export that image to the desktop and then decide to Delete the image you exported to your desktop the original images remains and yes you could/can still see it in LR and do more edits on it or remove and or change the edits you had previously done on it.
Please review some of the very good LR tutorial available on the NET and maybe even buy a book on LR.
thank you very much