Hi,
yes that’s always good to get a screen connected. 
Well the issue with the kernel and docker could be due to the kernel / software update that is done at the first setup. I guess this one should be related https://github.com/MichaIng/DietPi/issues/3425
Well it’s not a good idea to have Ethernet as well as WiFi connected same time. Therefore it would be recommended to use just one or the other. If you use Ethernet for the first setup, WiFi can be configured later on using dietpi-config. Quite a simple process 
If you like to configure WiFi as fallback for Ethernet, you might have a look to following tutorial https://dietpi.com/forum/t/using-ethernet-wlan-interfaces-not-at-the-same-time-in-v6-30/4251/1
EDIT: You might run into some timeouts for checking the internet connection. Do you see on screen what check is failing?