1. No. I suggested it to avoid any problems that may occur because you have a semi-functional phone.
2. The phone needs to stay connected.
3. If the phone is already on 7.1.2 as your second screenshot indicates then there is no difference. Either one will work.
There are IPSW files online you can download. I don't know where, others have provided links here before, but I don't normally suggest it simply because I am unfamiliar with the correct IPSW that you or anyone else should download. If I suggest the wrong one then there may be problems.
iTunes knows what you need however.
