Hello Richard, welcome to the forum.
I can offer some help to your project. There is a good resource that does cover starting x11vnc at boot time. It's located here:
You may also wish to consider TightVNC Server. I've used it in the past without issues when establishing a VNC connection between Ubuntu Mate and a Raspberry Pi.
There is a great guide on setting up TightVNC Server on a Raspberry Pi located here:
When I'm unable to establish a network connection of any kind, it usually boils down to one of two things. Either there is something wrong with the network configuration, or a firewall is blocking the service somewhere.
That being said, I don't believe that you will be able to establish a VNC connection to your Pi just by enabling a WiFi hot spot. Typically a WiFi hot spot will only pass along a Internet connection to other devices.
However, I have found a couple of guides that should help you achieve your goal.
This is all very interesting. Please post back and let us know if you get a working VNC connection working through your Pi's WiFi hot spot.