When composing a Tweet, you will also see the options to:
At the bottom of your home timeline you’ll see a navigation bar.
To set push notifications for your account to be notified when a user retweets, favorites mentions, replies to, DMs you or follows you:
Removing an account from the Twitter for iPhone app effectively signs that account out of the app. It does not delete your account. You can always add an account back later by using the Sign In button.
Check out the Advanced Tips and Tricks article for more fancy moves.