Hello MSFT, and welcome to Sevenforums.
What I understand of your post, is that some changes made by other admin user are bothering you. When a user can make changes in the system, it will affect you as well as himself and others. But focus on the specific topic you mencioned about the icons, when an user installs a program and selects the options of create a shortcut and/or add a shortcut to the start menu, the installer will do that to all the users (there are very few programs that let us to select just our user account). The most you can do to prevent it, is to advice the other user not to select the option of create a shortcut when running a program installation process. The shortcut could be then manually created by the user when installation finished, so it will only appear in his account.
Conclusion: talk to the other people that are using the PC about this or just take it easy and delete the shortcuts.