The module would need to support content plugins, the easiest way to do this is to use the following:-
$text = JHTML::_('content.prepare', $text);
where $text is the output text of the module.
If you use the custom html module that Joomla includes then this already support content plugins (in Joomla 1.6), there is no need to create one specially. Just add the embedding code to the custom html.
Yes the plugin can work with K2 articles and any type of article that supports content plugins.
Looking at the embedding code you show, you have made a mistake in the country parameter, it should be
count
ry=co.uk
also it should be amazonW
S not amazonWA
If you use an itemId then you don't need a search index or title or keywords parameter. Aslo if you have set the country and your associates id in the plugin parameters you don't need to specify them again, you only need to do that if you want to override the default values you have set.
You can just use
{amazonWS:itemId= B0030G30E4}
I suggest starting with as few parameters as possible, then expanding them as required.
You also need to remember to enable the plugin.