Answer to: Touch ID is broken, what can I do?You can replace the button and cable with a non-Apple part and your home button will work again but the Touch ID won't work. Your other option is to send it in to Apple to have them fix the Touch ID.
Answer to: iPhone disabled need to connect to iTunes wants a passcode entered onYour device is in Disabled mode: As your computer and iPhone don't have trust relationship (hence the "enter your passcode" prompt in iTunes) It sounds like you'll need to put your phone into Recovery mode and restore it from your most recent backup. That's pretty easy to do - see the last section of this page from Apple: https://support.apple.com/en-us/HT204306
Answer to: Something is strange after replaced the screen.I'm having trouble understanding your question, but it sounds like you may be having trouble with your iPad Mini 2 screen staying dark or turning off when your cover is on it. It's possible that the sensors in the new screen are detecting the magnets in the smart cover when it's fully opened (they're only supposed to detect the cover when it's closed). Does the same problem happen when the iPad is not in the case and doesn't have the cover?