Does the Kindle Paperwhite have an Internet browser?
Can you use the Internet on it (for things other than downloading books)? If not, do any of the Kindles have this feature? Which ones?
The Kindle Fire line is what you're after. They're Android tablets that can be used for playing games, web browsing, watching video and more.
They do have an internet browser.
However browsing on these things is a terrible experience. It's slow. You constantly have to zoom things to read them.
Don't buy a Kindle with an e-Ink screen like the Paperwhite with the expectation you'll be doing anything other than reading books.
Yes, you can do basic browsing on Paperwhite under its black-and-white screen. But WIFI or 3G internet connection is required.