Hey Zuckerton
The 4013 that iTunes displays is an error on the connection. Meaning the connection between the phone to the computer is failing. Check the type of cable you are using, I always use genuine Apple cables for restores because they allow the most power and faster data transfers. Especially if you are messing with an iPhone 7 you need a dedicated connection. Please make sure the cables from the LCD panel inside the phone is securely snapped into the Logic Board as this can cause the iPhone not to behave correctly since parts are not readable.
I also do believe the iCloud information the phone is asking is required for the completion of the iOS restore. Apple built in security measures that require things such as the iCloud and the secure restore so that no one just finds the phone restores it and calls it their's.
As far as the computer not recognizing the device itself when its being restored that is a contributor to the 4013 error iTunes shows you. You can try to put the iPhone into recovery mode or DFU mode if necessary to re-attempt the restore of the iOS.
Good Luck!