Most of what you are asking is beyond normal theme responsibilities – they are more general WordPress questions. When it comes to creating templates to display them, that is normally a very advanced custom WordPress theme (or child theme) developer question – way beyond the level of support we can offer.
BUT – Weaver Xtreme is in fact somewhat unique in its ability to display custom post types. (Using custom fields is 100% dependent on custom PHP coding or a specialized plugin in a custom page type or custom post type handler, and way beyond any support we can offer.)
Normally, custom post types are used by plugins to display custom content (e.g., Weaver Show Sliders). Often, there will be plugin specific shortcodes to display that custom content via a shortcode.
But if you use a plugin to generate custom post type content (the only way I know to do that), you can use the existing Weaver Xtreme Page with Posts. After you set a page to the Page with Posts template, you then can specify the slug of the “Custom Post Type”, and the content of those custom posts will be displayed using the default Weaver Xtreme post content display code. You can also do the same thing with the Weaver Show Posts plugin and shortcode.
But beyond that, using and understanding Custom Post Types is outside the realm of any theme. I don’t have any recommendations on tutorials on how to do all that. There are all sorts of plugins to manipulate and use custom fields – but again, we have no recommendations.