You can create Collections to organize your books by read/unread, and any other criteria you wish. Check the user's guide on your Kindle.
When you remove a book from the device itself, you're only removing the local, downloaded copy. The book remains in your account, and can be re-downloaded later.
Finally, there was a recent update that added a feature to automatically mark books read. Older devices may or may not get the update. Which Paperwhite do you have? You can select your specific model and generation here for update information - https://amazon.com/kindlesoftwareupdates.
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