Can an iPhone work as an iPod with better screen/storage/battery, if the LTE radio is removed?
In theory, it would be possible. In practice(as a bare minimum): - you need to patch the firmware for the new display - patch out the radio - ? patch battery capacity or re-init Not sure how much of the patching part is possible atm.
WiFi can be locked to whitelisted SSIDs via Apple Configurator.