For your first question use: http://hsqldb.org/
For your second question:
It is best to run Postgres locally. See documentation here: https://docs.mendix.com/howto/data-models/migrating-your-mendix-database#3-using-your-postgresql-database-in-studio-pro
To question 1:
What is the username and password to open a Mendix HSQL db?
With the Mendix admin password it does not work (username MxAdmin, mendix)-
Is there a specific need to access the database directly?
In Mendix it is reguilar practice to just add data grids or overview pages for any database table you want to view the contents of. Rightclick on an entity in the domain model and select “generate overview page”.