If I do a "force stop" on an antispyware program so that the app symbol continues to remain on phone, does this actually stop the app from being able to detect other apps from being installed?
Pretty much if you force stop an app, it stops running, so most likely it won't be able to do it's job. Not sure what you mean by "symbol continues to remain on phone"... where's the symbol (icon?)? In the app drawer, in App settings?