Those files on Google drive are only going to be your personal data and app data. It won't be a complete system backup of a previous version of the Phone's OS. If it's possible at all to revert your S7 to Nougat, you will have to flash the phone's firmware using Odin. But, as I stated, I don't know if it's even possible.
As for your texting problem, it could very well be that your first problem and your second problem are related. 'Emergency Calls Only' as explained means that your phone is having trouble communicating with your carrier network. This would also prevent SMS messages from sending since they are also handled by your carrier.
Three things come to mind. First, that you are in an area where you simply can't communicate with your carrier network or secondly, your SIM card needs to be replaced. The other thing might be a suspended, disabled or misconfigured account. If you are sure the account is up-to-date payment wise and you haven't reached some limit, then you might want to contact the carrier for a replacement SIM.