Selfhosted

If you're only looking to access the services locally, absolutely.

TL:DR, yes you can. But its not nearly as reliable as wired internet and is dependant on where you are.

I'm currently living in a place where only DSL is available for wired internet and its 1.5 mbps down at maximum so this is essentially my situation. I dont self host anything currently as I'm kind of in between projects but I could in theory self host something and access it remotely.

What I'm currently using for internet is a load balanced connection between starlink and lte. I'd recommend just using lte if possible. Starlink is good but it can be very spotty.

I'm surrounded by trees and the towers near me are old and go down more often that I would like or get bogged down so I need starlink but due to the trees it goes down frequently. Every minute or so. Sometimes I get 5 minutes of internet through it and thats fun.

I recommend getting a dedicated cellular router like the GL.iNet Mudi (but you're gonna need a USB Hub if you want to use Ethernet), Spitz (4G) or Puli (5G). The latter two have integrated Ethernet ports. Both are also available with built-in batteries.

Some people do it. For example we have this solar-powered website: https://solar.lowtechmagazine.com/

You'd need an energy source like a solar panel, a battery and some computing device. Like a single board computer (Raspberry Pi) you can also run webservers on smartphones, or even a microcontroller. The server part works without an internet connection. But you obviously need some way to connect to it. A wifi (router) or a computer connected via an ethernet cable.

The tech isn't too complicated. Just install nginx if you have a raspberry pi, open a wifi and put your website on it. If you choose a phone, try Termux and a supported webserver. Both Linux and smartphones are designed to even work without an internet connection ;-)

Of course, you just need to make sure your power supply, however it is set up, needs to provide constant power over long term that the system needs at minimum. That means for ex. if you use solar, you need to have a big enough battery and array so that it can charge batteries throughout the day even when it's cloudy so the system can be up overnight when there is no power generation happening. If you have for ex. a raspberry pi and a smartphone as a hotspot, you can probably have enough energy with an average UPS and one solar panel to make sure it will never go fully empty overnight, regardless how cloudy the day was.

I have a trailer (workshop) with solar power, batteries, a raspberry pi controlling everything and a cellular hot spot. It pumps all the solar, battery information and light controls over MQTT and home assistant over cellular. So yes its possible, what do you want to do?

At that point just get a GSM router

For public services you will need some kind of tunnel, as cellular networks or Starlink will not provide you with a public IP. Otherwise no big issue with an ARM SBC and a somewhat decent battery.

Note: I have not done any research on the topic, but I'm just theorizing based on what I already know, as it's an interesting mental excersice.

Obviously the biggest problems will be uplink and power. Solar and a battery bank is the obvious choice, but other methods of powers can also work, such as a small generator in a river, etc.

Lead acid batteries are relatively cheap, and building a 12V bank out of car batteries makes sense as there is plenty of off the shelf hardware available to invert or transform 12V into whatever you need. Charging it from solar will be inefficient, but it will work, and there is also plenty of hardware for this (tip: boat-related shops can help you out here)

As for hosting hardware we're of course dealing with the constraints of load vs power consumption. If you can go for something like a raspberry pi zero, you can run for days off of a single car battery with those cheap 5v cigarette-pkug chargers. If you need something more powerful, you need to scale up power accordingly.

As for uplink, the question is "How much" off grid we're talking. I will assume that there's at least GPRS coverage that you can connect to with a 4G modem, even if you don't get 4G speeds. Plenty of off-the-shelf hardware available here. If not applicable, just substitute with whatever is available, be it CDMA, packet radio, starlink (eww), or anything else.

I’m using USB Router ZTE MF79U + Raspberry pi zero 2W to self host some basic stuff, really efficient setup for off grid systems

As it happens, I've just finished setting up a system exactly like this for a completely off-grid setup. I needed a Raspberry Pi running Home Assistant to be completely self-contained to monitor an adjacent, larger system that is only powered up intermittently (close enough that the two systems have a common ground).

Short version: the Raspberry Pi and the Huawei LTE router I'm using for connectivity draw a steady 9W between them (there's a lot of monitoring going on). I went with an old pair of 80W panels in very suboptimal positioning, a simple MPPT charge controller and a 110Ah deep cycle leisure battery which costs about €45, €30 and €120 respectively. The system has been running a few months now and the battery had never, ever dropped below 12.4V. The Pi uses WireGuard to connect to my VPS so Home Assistant can be accessed with a web browser since the network I'm using on-site doesn't do public IP addresses.

This is entirely doable, but you may need to do some manual network configuration.