Docker: Local Databases

Just revisiting a couple Docker sandbox sites I started playing with a few months ago.

1: Can you create a local database with Docker? If so, how?
2: If answer to first question is ‘Yes’, can the local database be accessed with a third party app such as Navicat? With my current MAMP Pro set up I can easily back up my remote database at the end of each day to my local machine by dragging the tables to my local server. Can Docker be used in this way?