You can easily check if the buttons are working by a multimeter switched to a continuity tester mode (if you connect the probes you hear a buzzer sound). Then you connect the probes to both pins of the button (you should not hear the buzz) and you should hear a buzz when you press the button. There are 4 pins on each button in fact, while two pins are connected.
For connecting to the UART you can buy USB to TTL adapter , but choose one that supports both 5V and 3.3V as the UART on the ebook is 3.3V.
There are also interesting information about reverse engineering the ebook here:
https://www.synacktiv.com/en/publica...-reverser.html