I will try to answer some of your basic points, however I do not have an example handy that I can upload. Basically, a Type Extension applies to the type of object. For example; if you wanted to add a new method to the StringUtils component, you could create a Type Extension, and all StringUtils components in your solution would have this new method (or property or event). A Component Extension will only apply to that specific instance of a component. This might be useful for a particular control within an application where you want to add a method to evaluate its contents and return something about it. I have not really found a great use case for a Component Extension, as it is less flexible, but functionally identical.

In terms of how these relate to translators and UI Connectors; they don't really relate directly.

You can do pretty much whatever you want to a given control if you are adept enough at C#. For example; the CredentialStore component doesn't have a delete method. You could add one to it using an extension. StringUtils doesn't have a method for getting the matching RegEx values out as a collection. That could be added via an extension.