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Yes, BeeBase uses the sqlite3 file format. You can make changes to the sqlite3 file with other SW, but there are some rules to be followed if you want BeeBase to work with those changes. More info is in the manual here: https://beebase.sourceforge.io/index.php?page=documentation&...
Yes, it is close, although it is completely homebrewn and lacks a lot of functionality of common lisp. Think of it as taking the syntax from lisp, some basic lisp functions, and then adding functionality for programming your database.
True, this could be improved. Note though that if you hover over the text entry box, there is a tool tip that says this:
Name of the field. Must begin with an uppercase letter followed by further letters, digits or underscore characters. Non-ASCII letters like German umlauts are not allowed.