Installing Volume License Services on Now Windows 2016 server - Have questions

All,

We have an old Windows 2008 R2 KMS server that is aging and will not activate Windows 2016 servers. I have a new Windows Server 2016 box and I have installed the Windows Srv 2016 DataCtr/Std KMS key vial elevated command prompt and activated it successfully.

We also have Windows Server 2012 R2 and Windows Server 2008 R2 boxes in our environment as well as WIndows 7 PCs (soon to be Windows 10).

Do I have to install KMS keys for all of the operating systems I mentioned above? Will the Windows Server 2016 KMS key also activate older OS?

Also how do I install Office product activation to this host? We have Office 2010 installed right now with some 2013 deployments. If I install the Office 2016 components will that activate previous versions too? Or do I need to install something for both Office 2010 and 2013?

Thanks in advance!