How do I set up a Latest Items section to show all the newest added items that I have put into K2 items section on my Joomla site? I tried to set it up but the only categories to choose from are from the Article Manager and not the K2 manager.

From a menu choice use K2 Category and set the item ordering either in the category settings or if using multiple categories, in the menu paramaters.
If you are building a module, chose mod_k2_content from the module manager and place a module where you want it

great - worked ok, thanks.

welcome