One other tiny point: do you know offhand why I have this WPML symbol/menu in my admin bar? It is always empty when I hover over it, and the menu contains no items. I would like to get rid of it if it doesn't hold anything useful.
The WPML menu item in the top admin bar that you're referring to, is shown when the WPML automatic translation feature is enabled and shows its status information.
There is no built-in option to disable it, but you can include some custom CSS code in the admin area, to disable/hide it.
The above code snippet can be included through either the active child theme's 'functions.php' file or through any other plugin that enables including custom PHP code.