So if an app is in the app tray on the bottom is it running and using system resources? How do I kill it (enter the app and hit home to exit out?)? How do I know if an app is backgrounding?
Not all apps in the system tray are using resources, no. Knowing whether an app is backgrounding or not would vary by app, but if it's concerning you, hold your finger on the "running" app until the close button appears and kill it.
So if an app is in the app tray on the bottom is it running and using system resources? How do I kill it (enter the app and hit home to exit out?)? How do I know if an app is backgrounding?
Apps only background if they have something to be doing. If it's a music app, it'll be playing music, easy enough to tell. If the app is downloading something, it may complete the task before going into a freeze state. If an app is using location services you'll see a little GPS icon on your menu bar. etc, etc.