You can connect with no internet, but you have to do some networking backflips. You’d have to set the pi up with a DHCP server and as an AP, and you have to know the IP of the pi from your phone. It would be easier if you just hooked up an old router to do the DHCP and AP. Then connected the pi and the phone to the router. Your phone might get confused when there’s no internet…
I installed the adafruit touch screen on my pi and it wasn’t nearly as smooth as octopi in general. I wouldn’t recommend it. It’s much better to just have the LCD on Marlin and a web page for the pi.
There is a plugin for octoprint called “TouchUI” and it slows loading a little, but it make using it with a touchscreen, like a phone much easier.
You can also easily use the gpio on the pi to control relays. Things like powering off the Marlin after a job is pretty easy to script. I have a tutorial on thingiverse about it (I’m not at a computer but if you look at the jeffeb3 “things” you’ll find it).
The best part of octopi though, is that you can just upload the file to the pi from your CAD/CAM machine. No more SD cards!
Lastly, the other thing I did (which is more advanced) is to move the log files, configuration, and gcode storage to a USB stick. The sdcards can easily get corrupted in a pi after a year or so. Moving the storage to a USB stick makes them last a lot longer.