When I first set up my pNode, you couldn’t use a hotspot. Is that still true? And can you switch it to a new WiFi network from the one you originally set it up with?
Also, if I set my pNode up using Ethernet cables is it true I can’t run it off my WiFi without them?
This is not advisable because you will eat through your mobile data with a quickness and be faced with a massive data bill at the end of the month.
You can give this a try:
If Wifi is successfully setup, you can connect/disconnect Ethernet as you desire. The pNode will use the more stable connection of the two. I suppose if Wifi wasn’t successfully setup you could still disconnect your Ethernet; your pNode just wouldn’t do much. 
Just to clarify on the “having to stay on Ethernet” scenario.
Earlier on when setting up a physical Node using the app was a bit problematic for many people, we suggested the manual approach using an Ethernet cable. This approach is different from the regular setup, and does require the physical Node to stay connected after successful setup.
The other way around does work. When setup using the app was successful (just using WIFI), you can connect through Ethernet afterwards.