On step 36 of this guide there is a little black sticker over the home button connection with the screen assembly. Did you reattach this sticky tape after assembling the replacement screen. There could also be a question over the reliability of 3rd part screen assemblies, you have proven that the home button works when using the original screen so as long as you have transferred all of the components from the original screen across to the replacement screen then the issue is with the replacement screens.
As far as I am aware the only way to restore an Apple device that has been disabled by entering an incorrect passcode numerous times is to connect it to iTunes. If for whatever reason you can not install iTunes on your computer you can use another computer or even pop into an Apple store and use one of their display models to restore your phone.
Sound like the LCD has been damaged/become faulty, you can follow this guide to replacing the LCD, when ordering a replacement part i'd recommend you order a replacement Digitiser too as its very easy to tear the digitiser cable or to shatter the screen if youre not careful or have not done this before. Links for parts iPad LCD iPad Digitiser
Try replacing the power brick using this guide, if after this its still not working then your looking at a CPU/GPU faults, and its going to be more cost effective to buy a second hand unit than to repair.
In short yes, it seems apple has programmed something into iOS 11 which detects 3rd party screens and causes the operating system to "malfunction" its has various symptoms such as digitiser only responding to every second input for example. I have had some success in restoring through DFU mode, but only on a few phones. My company has stopped iPhone 7 screen replacements for this issue.
The button is separate from the cable, on the back of the digitiser you'll see the home button bracket just use a metal spudger to break the clue holding the bracket to the digitiser, the button will now be left, your replacement cable will likely come with the bracket attached so just connect to the logic board and glue the bracket to the digitiser positioning it correctly over the home button.
I just had a similar problem on my D5100 and was advised to send it back for repair. After comparing mine side by side to another at a camera shop, (remove lens and with camera on press shutter release button) the lower right corner of the mirror was binding with the stop. We were able to GENTLY pry the lower right corner of the mirror away from the stop (from the right, not underneath) and now it is functioning flawlessly.