You want an admin user?
Set up a user with different rules, read/write everything.
You should then be able to call the folder "users" and everything in it as that user.
When you make your call to the database, keep checking the content of responseContent, and look at what the dictionary is. You may need to adjust your key/value blocks accordingly.
I don't know enough about the deeper inner working of firebase rules to advise.
This is not really an app inventor question, it is a firebase rules question. You will get more luck on stackoverflow. Don't mention App Inventor or tag it as such (this will only confuse the issue), just say you are using the REST API to access the data.
Perhaps change the rules for the users node, so that all users can write to the users node, but they cannot read it, setting your admin users rule to be able to read the users node? Maybe that will work?