Error while entering Apple ID (entered someone else's ID)
You seem quite panicked and distraught. Your question was very confusing and you may have misunderstood the situation, but from what I could have gathered I can provide these pieces of advice:

The old owner may have incorrectly removed the device from their iCloud account. This is a very easy mistake to make and has happened many times before. To correctly remove it, both you and the old owner need to carefully follow the instructions here (under &quot;If you no longer have your iPhone, iPad or iPod touch&quot;) otherwise the device may never be recoverable.
You may have misread the instructions and inputed the incorrect information into the incorrect fields. Press the back button on the screen until you return to the language selection screen and setup using the instructions here. Preferably, to reduce confusion, use quick setup, to auto-setup wi-fi and iCloud, if your wife (not you) have an iOS device, other iPhone, iPad, or iPod touch, running iOS 11 or later. You can find the version number by going to Settings &gt; General &gt; About &gt; Software Version.
You may have somehow broken the setup instance and the device needs to be reset. To do this follow the instructions here while making sure to choose update (if available, otherwise choose restore), when prompted. Note, this requires you to enter recovery mode, and should be perfectly safe provided the connection isn't interrupted (e.g. unplugging or turning off your computer) while the device is restoring. You shouldn't have to use DFU mode. Once you return to setup, follow the instructions above in part 2 to setup your device.

If after following these steps, you still can't setup the device, your best option is to go into an apple store and get them to correctly assess the issue your having and get them to fix it.