How make a standalone field with no Entity or Bundle? I want to add a custom configuration form to my module; I don't know if making a custom schema is better or if I should make a standalone field and use its different field APIs to deal with the value.

Can I create a standalone field with no entity or bundle? If I can't, what would be the alternatives?
Take a look at system_settings_form and how it is used by other modules to create a basic form and field for module configuration. It'll generally use variable_get and variable_set to get and store it's value.