intra site modules are simply custom user controls (ascx) placed into backend pages to add your custom functionality to the backend. To copy the look and feel of the rest of the site, I literally copy and paste the HTML into the control.
I did a webinar on this a while back, including code to recreate the backend editor. It appears to still be valid, and is available here: http://www.sitefinity.com/blogs/joshmorales/posts/josh-morales-blog/2011/06/30/sitefinity_intra-site_module_webinar_notes
the centered view is a bit different, and I don't have that html, but you could potentially do the same (copy it from another native page). I don't always get it 100% accurate (my controls are usually laid out different from what Sitefinity does) but I get close enough so that it doesn't break the user experience.
The actions menu could be recreated with javascript, but if you are looking for NATIVE integration that does all this for you, indeed you would be looking at inheriting or much better yet: simply using the module builder, which lets you build custom types that automatically install themselves into Sitefinity as if they were regular modules.
Fields are definitely designed to run inside the context of native sitefinity module definitions (the classes that make up the UI using the Sitefinity context). This doesn't mean you can't include Sitefinity content in your modules; it simply means if you do you'll have to implement the integration yourself using the API.
On your last question, the only way to use external data but still keep the "Sitefinity Content" UI is to inherit from Content, then create a custom provider that reads from your database and translates it into the Sitefinity content type. It is certainly possible, but is quite a big project.
Unless you are in full need of this tight integration, I recommend simply going intra-site, linking to Sitefinity content types,taxonomy, etc through the API and manage it separately.
I hope this was helpful!