How to link other tables (entities) to parent and child categories?
I am going to suggest an alternate solution.

Rather than trying to mock-up a database design in Visio, why don't you create the database design in the relational database? Once that is complete you can use software to create the database diagram from your actual database. Most relational databases have database diagrams built in, and if the built in diagrams don't fit your needs there are a variety of third-party alternatives, many of them free, or with trial periods.

The advantages to this approach is that doing the actual design will help you think through your choices, and even if it doesn't end up being the final design, you can use the work as a starting point.