I’m afraid I don’t know how far the Pi can be from the screen. I only ever use without a screen. I suspect what you are trying to achieve may be too far, but someone else could maybe advise. I know people can run HDMI for upto about 10m but the touch screen uses a different cable that may be more limited.
In case you haven’t found them already, there are some links that may be helpful to decide on the hardware and setting it up:
For the hardware you could take a look at this:
And instructions here: