Vit, I think you are asking to do something that would take a lot of knowledge and programming skill.
For a start, to make an integrated screen using both screens requires the application and combining of two completely different technologies - one having full colour capabilities at a high frame refresh rate, the other is limited to a small number of greys and white and black with a frame refresh rate you can watch.
To answer your last questions. I think I can see what you are after but there are easier ways of inputting text - I use a small USB keyboard that packs in the carry bag with my EE.
Is it possible? All things are possible if you throw enough money and resources at them
In fact the question should be. Why would we want to do such a thing?