I'm having a hard time animating the camera movement with the empty object. The camera (see the included video) is always turning on itself as oppose to do the rotation around the cursor axis which is where the empty object is....and also the empty object doesn't seem to impact the camera if I select it on its own....what am I missing?
Click to see : Video
It seems that I fixed it by making the camera a child of the empty object which now that I'm watching it seems to be what should've been done.....let me know if I got this wrong.
You can do it either way, but in the video I noticed that you animated the rotation. It seems intuitive since you only rotated it, but that rotation was based on the 3d cursor and not the origin of the camera, so under the hood you are both rotating and moving the camera's origin at the same time. If you key location and rotation you should get the right effect!
Parenting it is another valid solution, so if that works in this scene then stick with it!
In Blender v2.82 I've run into an issue with the parenting shortcut CRTL + P. Didn't seem to matter the order I selected the camera/empty or empty/camera it would always set the empty as a child of the camera. This hung me up for a few.
Instead, in the Outliner, I drag the camera over the empty - when dragging a tooltip pops up up indicating you can hold shift to set what you've dragged over to be the parent of what you are dragging. So, hold shift and drop the camera on the empty, and it's now setup with a parent > child relationship.