How should one implement add_settings_error on custom menu pages?

The Professional WordPress Plugin Development book explains in detail how to properly use the Settings API, and it also demonstrates how to add Menus and Submenus, but unfortunately it doesn’t provide any joined-up examples of this. Whilst I’ve managed to get most of it working, I can’t figure out how to properly implement add_settings_error on custom Menu pages. Here is my code:

How to Use Checkbox in Custom Option Page Using The Setting API

Can you please let me know how I can add a checkbox to Setting API in creating Custom Options Page? I am using the following code to add a txt box which is working perfectly but I am totally confused how to add chechbox to the setting API and options. I just tried ti update the input type to checkbox but I am not sure what to put in Value besides when I save the form the check box still appears unchecked!