If your books have DRM (digital rights management) it must be removed. Then Calibre can convert the books. When you install Calibre it will go through a Wizard and select the Kindle when you get to that part of the Wizard. Then Calibre will convert to mobi format (preferred format which is essentially the same as Amazon's azw format).
Book covers will not show on the home screen on the Kindle. When you open a book it will automatically go to the beginning of the text. If you want to see the cover, you can, while in the book, hit menu and select cover. After you finish looking at the cover, hit back and you'll be in the book.
Calibre is simply excellent at managing your library. You can add tags to make it easier to sort your books.