Thanks for using WP Socializer.
I see that you are using AMP. But unfortunately the plugin does not support AMP right now. However it seems the AMP page already has share icons (not added by WP Socializer)
Regarding facebook count, can you please ensure if you have set the facebook APP ID and the APP secret in WP Socializer –> Settings page ?
You have to create a facebook app and add it’s details like below.