Hi, I am Dave, I will help you with this.
1
If you restore from the system image, you should just need to log into Office with your Microsoft account and it will activate.
1
When you first installed and activated Office that licence should have become associated to your Microsoft Account online and it is from there that you can re-install Office without the need for a product key:
https://account.microsoft.com/services/
Do you see your Office licence listed there?