Use the official Apple cable if you still have it, or borrow one from a friend as the cable is usually responsible for error 9 to occur If that doesn't work, it might also have something to do with the IPSW you are trying to restore with. Try using a different IPSW or using Redsn0w to boot Pwned DFU mode and restore it like that. Error 9 can be related to the RAM disk kernel rejecting the ASR because it is not signed properly, thus breaking the connection with the device and causing error 9.
Did you disconnect the batter before repair and connect the battery last after the repair? This can happen if you have damaged the home button flex. Maybe the first screen was faulty but when transferring components to the new screen then you may have damaged it the home button flex. Another reason could be you somehow damaged the battery when repairing the screen however that isn’t very likely to happen.
Yes it will fix it if it’s not a faulty screen but a logic board will cost you as much as a new phone better off getting it repaired from a place that offers micro soldering or just buying a new phone.
Firstly when you buy a screen it will come with both the screen and digitizer. Which is fine and you can easily assemble this into the phone, if you replace with a LCD instead of OLED then you will notice a change as the LCD is not as sharp as OLED and the LCD also uses a backlight which OLED does not
The new logic board can be iCloud unlocked and network unlocked although you would need to check which board you are buying. I would recommend selling your phone for parts and buying a new phone as a logic board would cost as much as buying a new phone.