Where are entities stored in MySQL by default?
There's no default as such; each entity type defines its base table and field data table via the *EntityType annotation. See Structure of an entity annotation for examples.

The Entity API and its power don't just live in the database, there's also plenty of code involved to prepare things sensibly for the system to use inside a request. 

With that in mind, you might consider that using the built-in REST API is a more efficient way to communicate with Drupal than direct database manipulation, which won't give you the full picture of an entity without re-implementing at least some of the PHP logic in SQL