Hi LuluButtons, the S3 may not have a red star as a notification like your previous device. You will see a notification... what you see is what you get I guess
Twitter is likely asking you to set up the e-mail account IN Twitter so you can e-mail from within that app. I think: I don't tweet, so somebody else more experienced can chime in on that one.
Your edit suggests that you no longer need to know how to exit out of an app or close apps. For the benefit of our S3 readers: press the home key and that will get you back to the home screen. To close apps you no longer need open, long-press the home button and a list of open apps will be displayed... just swipe away the ones you don't need open anymore. That will free up memory.