When was this app taken off from Play Store? If this application was installed from Play Store, would it still show up in my installed programs after Play Store stopped offering it?
Play Store does not have anything to do with your installed applications. It just tracks and lists them on the website. You can keep your application in your phone even if it does not exist on the Play Store anymore.
Mobile spy is an invisible spy software for android.
Sure! If you have installed it from your Google Play Store, It will still show the history on your account after the play store stops it! But I'm sure such kind of spy app like iKeyMonitor will be allowed by Play Store.