Mongodb database design
16 MB is the maximum size of single document, e.g. one user.

The size of the collection is limit by maximum database only.

https://docs.mongodb.com/manual/reference/limits/

So logging to the database should be no problem. In my opinion using sensible indizes including _id is superior to a heap of collections.

It is not clear to me what you actually want to store in your database so I cannot really comment on the structure. Generally speaking there are three ways to handle relations: Using arrays 


storing subdocuments or 
ids of documents (You would have to retrieve those via a separate database request)
invert the relation by giving all referenced documents a field containing the parent document id


If you give more details, chances are somebody can give you a more detailed answer.