A nice feature would be the ability to add more snippets to the snippets page, for example custom codes such as a Windows Media Player embed code or something similar, just a page where we can add our own code using tags such as http://example.com/stream.php?user=$user (For automatic generation of particular links depending on the client username?

Sure, edit www/system/templates/snippets.tpl and modify to your tastes.  Examples for inserting the account info are in www/theme/quick_links.tpl.