- If you delete or move any folder or images outside Lightroom from their original location then you would see an exclamation mark on your image and a question mark on the folder where they reside in Lightroom.
- According to your workflow you first get the images from Photo app to desktop and import in Lightroom. At that moment Lightroom points towards the images you have on your desktop.(original not edited one). The source file for Lightroom would always be the folder where you have stored the dragged images from Photo App.
- Lightroom does not keep any reference to the exported images. So just leave the edited copies(export) in another folder.
- If you do not want the files to be at your desktop once you export them with edits from Lightroom. You can remove the folder(original folder) within Lightroom which will delete the images from your desktop as well as Lightroom.
This is a rather cumbersome workflow, and certainly not the intended way to use Lightroom.
Nevertheless, if you delete the original photo from within Lightroom, your problems ought to go away. If you delete in your operating system, then you have the problems you described.
If I were you, I'd strongly consider changing your workflow, including using only ONE organizing program, either Photos, or Lightroom. If you use two such programs, then you have introduced a lot of extra work moving back and forth that isn't present if you use only a single organizing program. THere's a lot of information out there on better ways to use Lightroom, including Getting Started with Adobe Photoshop Lightroom 5 | Adobe TV.