Is it possible to add css class to the page's body tag with rules when certain conditions are met? I seem to have read that there is a way of making Rules add a css class to the body tag, but I can't find out how to do it. Any ideas?
Yes - the Context module allows you to add CSS classes to the body (Theme HTML condition) based on whatever events you specify. You would then combine this with the Context Rules module which extends Context to allow for context events from Rules.