Can I have the Post/Page options in my custom post type
No. Custom single post types options section, including Post Options, Page Options, Portfolio Options, News Options, and Product Options are only available for their respective post type and can not be added to any other post added by any third-party plugins.
The reason for this is that these options are based on the options available in the Customizer panel and handling the custom post type is simply impossible.
That being said, we have plans to add some of the general options of these option sections for other post types in the future updates.