1. Err, they're used on most major websites. What you do is, you add that site's RSS feed to your RSS reader (like Google Reader), and it will show you new articles posted, as they're posted. This becomes invaluable when you check more than 2-3 websites regularly. For instance, I have a lot of tech sites (Engadget, Ars Technica, etc), and a bunch of webcomics (xkcd, Penny Arcade, etc) in Google Reader, and I just check it every morning to see what's new. It's especially nice since reading in Google Reader loads a lot faster than dealing with loading each individual page.
2. This is impossible to answer in one paragraph, but there's a reason that GMail is basically the most popular email service. It's got labels, great automatic spam filter, integrates Google's search prowess, works on a "never delete" concept (instead, you archive it out of your inbox, but you can still find it if you ever need it later), has decent filter functionality, it created the concept of conversation views for emails, ridiculous amount of storage, etc. It can even help you move your email over. You don't HAVE to use GMail, but I've moved all my mail over to GMail. It's just so convenient.
4. Google Docs is basically web-based document editing. Word processor (with MS Word document support), Spreadsheet editor (with Excel support), Presentation support (with Powerpoint support), and it stores your documents online so you can access, edit, and view them anywhere. In addition, it also supports sharing and collaboration, so you can edit a word document, for instance, with other people, at the same time, live. You actually can see what they're typing as you edit.
Yes, it's all free. There's very little Google offers that ISN'T free, and it's explicitly stated. The only thing you can really buy from Google is extra storage space for your account (shared among Picasa photos service, GMail, etc). Although frankly, the many gigabytes of data they give you to start with is more than enough for most people (ever had 7GB of email? I haven't).
Easy is a relative term, but frankly I doubt it'd take you more than a minute if you type fast enough. It's only like 5-10 questions, including username/password
Yes, that's exactly what I avoided. I'm not friends with 99% of my school, and frankly I don't care what they think of me (I didn't like most of them anyway!).