Let's say I make a shortcut in the Start Menu. Done. Works, and done.
Now I copy that to the desktop but it isn't working like you noted. I wonder if you didn't copy it but it was a "link" to the item in the menu. That could result in what you noted.
-> ANOTHER area I found was the folder the app starts in changed if it was on the desktop or on the start menu. It's a lot to ask users today but small things like that can break this.
But you ask how to control and fix all this. I think you'll have to dive in and write an app to correct what you find wrong with the shortcuts, remove links and place shortcuts instead. That is you become a software developer.
I am working with a fresh W10 install. I am used to W7.
One old (x86) application I run requires that I configure the Start in setting for the shortcut that launches it. The shortcut that was placed on the desktop did not let me change that. The shortcut in the New list does not let me change that. The shortcut in the All Programs list does not let me change that. Right-click does not offer Properties.
I created a new shortcut on the desktop. That lets me open Properties, so I was able to make the required change to Start In. That shortcut launches correctly. However when I right-click in that shortcut and Pin to Start, launching from the Start menu does NOT launch correctly (which is to say, the program is not started using the Start In value). Apparently the property I changed is lost when the shortcut is move to the Start menu.
How can I control the Properties of this in the All Programs, Start menu, and other places where right-click does not give the the Properties option? How can I keep a change to Properties from being lost when an item is pinned to Start? Is any of this even possible?
Thanks!
RH in CT

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic