Case a la display using the processor of any smartphone, is it possible?

Question

Do it yourself

Hello, I'm interested in the question of creating a device / case that will work from a connected smartphone.
What difficulties may arise?
The option of a live broadcast (a la teamviewer) of the smartphone display to the device using wireless networks was considered. Are there any chances to make a wired data transfer , for example, via Lightning (connector) (apple), to the device display ?
Is it possible to make a direct output of data to the display of the device without using the main display (smartphone display )?
The idea is to create a device a la a smartphone case that has a display, modules for data transmission using Wifi, UWB, 4g and other wireless technologies, as well as its own battery. The basis is a device similar to a smartphone, which does not require an OS, but works from the smartphone system. Question for what?
By holding a smartphone with this case, I can use the display of this unit with my smartphone without using my smartphone's display (energy saving). Further, using wireless technologies, leaving the smartphone at home (for example) and using it at a distance using this device.
Another example, the main part (display and all accessories) will be removable from the case, making this part waterproof, making a device with a camera, a person will be able to shoot video underwater, being on land and watching the live broadcast of the shooting through his smartphone.
Use this device for video conversations (a la Skype) using the rear camera (which is many times better than the front one). Fans of selfies (a la selfies) will be able to use the rear camera, while seeing what they are shooting by looking at the display located on the back of the phone, again, do this for better photo quality.
The options for using this device are quite extensive.
((Full wireless touch display)

Answer 1

From the phone, you can only power the power to the case ..

Answer 2

Look at the implementation of a phone case with an e-ink display

Answer 3

Without an OS and with a disabled display, there is no donor :)
In any case, this is a “brain” device with a CPU and a wrapper in the form of a wifi screen, etc. and "do not consume" the energy of the donor, it will be at the expense of the energy of the device itself, that is, in total more than the donor. Here the idea of ​​​​a "cover" with an additional 10 amp battery is more suitable, it will be a good idea.

Answer 4

Theory is bullshit. Too energy- and resource-intensive.