Yes. Since this laptop runs ChromeOS, everything must be done through the web browser. In the case of Amazon's Kindle or B&N's Nook platforms, you would buy the ebooks from their respective websites, and read the books through their web interfaces. Amazon's is called "kindle cloud reader" (https://read.amazon.com/), and B&N's is called "nook for Web" (www.barnesandnoble.com/u/nook-for-web/379003594/). Google Play books, Kobo books and other major ebook retailers have similar web systems so that you can read your ebooks on a Chromebook.
Yes. The Chrombook offers "Chrome Extensions" which are just like mini programs (that's the most simplistic description) that run in the chrome window. There is a Kindle extension so you can read kindle books on your browser but I was not able to find one for Nook.
Yes. With the Kindle you can also download a book to the Chromebook and then, via the USB cable, transfer it to the ebook. No need to read it on the Chromebook. This requires a little knowledge of the Chromebook and the Kindle file systems. Don't know if this is possible with the Nook.