1. It is called Tweeting and anyone who has a Twitter account can see your Tweets, unless you lock your account, in which case only your followers (who you approve to follow you) can read them.
2. On Twitter you have followers. If you follow someone you can see all of their tweets either on your phone or computer. If someone follows you, they can see all of your tweets. You can follow someone without then following you back.
3. To follow a person on Twitter, just search for them, click on their name and then click the follow button.
4. You could use this for education by having faster up to date information, like if class gets cancelled or if assignments change. Most phones can have Tweets sent right to them so as long as all of your students have phones and a Twitter account you are golden.
5. Twitter is like a company, so you capitalize it like you would for fast food chains or any other company.