1
The best option is to uninstall Office from your old PC if you will no longer be using that PC.
If you will still be using the old PC, if you have a Microsoft 365 subscription, not a standalone version of Office, you can install and use Office on up to 5 devices at the same time.
2
If you use OneDrive to sync your files online, then if you log into Windows and Office on the new PC with the exact same Microsoft account, OneDrive should automatically sync your files down to the new PC.
If you do not use OneDrive to sync your files, you will need to manually transfer your files form the old PC to the new PC using a USB flash drive.
3
When you first activated Office that licence becomes associated to your Microsoft Account as a digital licence online and it is from there that you can install Office on the new PC without the need for a product key:
https://account.microsoft.com/services/