re: “Error: This license is at its activation limit. Deactivate a site before adding a new one.”
You can not add the support license key to the second site. You need one license per site. That said, you can install cMap on the second site but you can not use the support key on multiple sites. So, do not add the key to the second site. cMap will function without the key being registered to the site. The features that it will lack will be support and updates for that second installation.
re: I had a questions about the “licence expiry date” which for my current cMap is May 15, 2016. Is this about the support and updates service, or will the plugin itself stop working after 2016?
This is just for support and updates. Opting to renew is up to you and is not required. However, it is highly recommend because without that you will not receive updates which would fix any bugs that might be found, security issue that might be found, compatibility updates in case an update to WordPress or Connections breaks something and the template needs to be fixed to work with change in those platforms.
Hope that helps! let me know.