Hi
K2 is an extension and therefore works within joomla. K2 will work on any template, it just has a default styling which is inherited from the joomla template. Some templates have added extra styling typography for instance. The tutorials will show you that you can change the order in which content is displayed. (I was very impressed when I first went through the tutorials last week and I am sure that I will learn even more when I view them again)
The K2 web site
getk2.org/documentation does have documentation on template design etc.
Other modules such as gavicks newshow pro will allow to to change the order of the content - to show or not show titles, images, extra fields especially at category level.
Why do you want to use K2? The joomla core is often more versatile and simpler to use.
Regards