In order to be able to use the Kindle store and the experimental browser you need the latest firmware release for a Kindle Keyboard 3 which is 3.4.2 at present. You can see more details here:
https://www.amazon.com/gp/help/custo...deId=202048000
There have been no further updates to this firmware for several years. As the AZW3 format is the latest supported by this device, you should have no problems using Calibre with it. There is a jailbreak for this firmware and you should have no problems using it to allow you to load whatever of our enhancements you want.
Dave