Well, you certainly got my attention.
All Chromecast devices require a network (preferably WiFi) with an internet connection. They all work on 2.4GHz networks and most of them (all but the older versions) also work with 5GHz networks.
You can screen mirror Android phones to them using these instructions:
https://support.google.com/chromecast/answer/6059461
Note: mirroring does not work with EVERY app. The only way to know is to try it.
You cannot mirror at all on an iPhone. Sorry, Apple declined to support that.
Google does not officially support the use of HotSpots for internet access. But, some people have reported that it works fine.
There is a trick... most phones can't BE the WiFi network and act like they are ON the network at the same time.
So, you will probably need another device
Turn on the WiFi hotspot on your phone to make a new network (note: this HAS to have full internet access)
Connect your other device to your phone hotspot
Use the other device to setup your Chromecast to use the phone hotspot
Use the other device to cast to your Chromecast
A couple more warnings... as I said, your hotspot has to have internet access. Chromecasts require this even when you are casting local content. Be warned that Chromecasts can use a LOT of data quickly. Because of this, speed of connection is important. Even if you have "unlimited data", some providers throttle phone data speeds when you do a lot of data. This will impact the quality of your casting or cause a lot of stutters.
Honestly, in the field, you would probably do better with a cabled solution and avoid all the extra hardware. Try to find a video cable that connects your phone to your monitor. Also, Chromecast devices are designed for use inside the home. I've had issues where I've taken one of my Chromecasts outside and it overheated from being in direct sunlight.
Good luck finding a solution.
