Change an app from "all users" to "this user only"
You have two questions here. ( and ~ is short for the /Users/current_user folder)
1) For apps only to show up in your account - move them to ~/Applications
2) If a user is not part of the Administrators group then that user cannot install apps in /Applications which is the normal place for shared Applications. Non admin users can install apps in their home folder ~ but not another user's Applications folder nor the system Applications folder.