If you create a new customer using the WooCommerce REST API, it will create a new WordPress user of the role Customer. Email is unique, a new customer cannot be added if his/her email is used by another WordPress user whether a customer or not. I tested that using API.
Regarding password, I still did not receive an email with it. I have my own WP deployment, ...
WordPress does not support uploading SVG images. You may find plugins that enable this but SVGs can be dangerous and can contain malicious data.
Your problem has nothing to do with filesize. You should raise an issue with the SVG plugin you installed
Where are the admin notifications stored?
They aren't. Admin notices have no storage unless you implement it yourself for your plugin/theme.
WordPress provides hooks and styling for displaying admin notices, but that's it. It might provide styling for dismissible admin notices but it provides no storage or registration mechanisms for persistence.
And when ...