Quick Answers

How to hide empty categories?

It's not possible to hide empty categories in DOCman, if you want to hide an empty category the best approach is to un-publish it, or change the permissions so it's only visible to administrators. 

The reason for this is a limitation of the Joomla permission system. It's not possible to determine in a performant way if a category has no documents or the documents it holds are not accessible by the logged in user,

How to add a frontend document counter?

It's not possible to add a document counter in the frontend. In the backend we don't consider permissions we just count all documents, in the frontend we would need to consider permissions to get an accurate count, this is technically not possible to do in a performant way with how the Joomla ACL system works.