I’m wondering if it’s possible to easily count the number of rem (/cards/bullet points) per document?
It is! 
Type /metadata inside the Document’s Title. It will specify the Card amount it holds in the upper part of the page:
While it won’t count the Rem number either, and it may be a bit old, the Word Counter plug-in may be something you’d also be interested in: How do I activate/view word count? - #3 by Gabriela.AD