How do I link to an internal page?
[Link title]({CCM:CID_xx}). Where xx should be replaced with the Page ID.

How do I embed an internal image?
. Where xx should be replaced with the File ID.

How do I create a link to a downloadable file?
[Link title]({CCM:FID_DL_xx}). Where xx should be replaced with the File ID.

Can I still use HTML inside of the Markdown editor?
Yes, that's possible.

How do I add proper styling to the HTML output?
You could for example take a look at one of these CSS styles: http://mixu.net/markdown-styles/ and integrate them in your theme.

I am a developer, how can I add snippets?
I'd recommend taking a look at this addon: https://github.com/hissy/addon_basic_snippets_pack. It can easily be extended and works seamlessly with Common Markdown.