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Do I need to wrap this my code in <code> block?

No. Instead, wrap your code in a <pre> block and then use [code lang="lang"][/code] to wrap your code.

How can I customize the code block layout?

In the Wordpress Admin interface, under Options -> Code Highlighting, you can specify a custom CSS stlye to wrap your code blocks in. While the preview button is nice, Firebug would be the tool I would recommend.

Can I use this with custom wordpress themes?

Yes; however, you might need to do a little bit of tweaking. JR found that CodeSnippet automatically adds a link if you're theme is using wp_head; however, if it isn't, you'll need to add the link to the codesnippet/codesnippet.css stlye sheet to your header and you'll also have to define the 'codesnip-container' element. The default value is: border:1px solid #ccc; background:#eee; padding: 5px;margin:10px;