If I move a photo from my Photos App to my desktop and then trash the photo from the Desktop, does the photo get deleted from the Photos App when I empty the Trash?
I often move a Photo to the desktop from Photos App. I use the photo on the desktop for a project the I am working on form several things. My question is if I move the photo on the desktop after I am done with it without saving, and empty the trash does the phot become deleted in the Photo Library?
That depends on what you mean, exactly, by "move." If you drag a photo from the Photos app to your Desktop you aren't moving it, but exporting a copy of that photo as a file, and storing it in your Desktop folder. You can see that the photo is still in your Photos library. You now still have the original photo in your Photos library, and an exported copy in your Desktop folder. They are separate versions of the photo and no longer connected to each other in any way. What you do to one won't affect the other.
This is easy enough to try for yourself. Drag a photo from your Photos library that you don't care about to your Desktop. Then observe that you still have it in Photos. Then delete the one on your Desktop. Look in Photos and you'll see it is still there.
If you mean something different by "move," then let me know exactly what you are doing, step-by-step.