Did you connect to the HESTIAPI WiFi network to enter your WiFi name and password?
If you did, download a network scanning app like Fing and scan your network 5 minutes later to find the HestiaPi IP. There is an option to show open ports on it and you should see at least port 8080 and 22.
If entering [YOUR_HESTIAPI_IP]:8080 on a browser brings you nothing, try SSH (download putty) to the same IP (without any port numbers) and login with pi and hestia as credentials and run these commands entering hestia as the password if prompted again:
Absolutely not.
LCD and relays are somehow optional. For a standard use of a thermostat though one would need at least 1 relay. For testing like you do, no you don’t need them.