I think you are going about this all wrong. You shouldn't be using Jumi to run php in your articles. You should design a component. Although this will take a tiny bit longer to setup initially it will save you time in the long run and prove to be much more flexible than using Jumi in a single article. Have a look here on how to create a Joomla component - http://www.joomladevuser.com/tutorials/components.
a href= tags should not be any different from any other html you have ever used.
echo '<a href="http://.....">link</a>';
To make just the frame/div/table/etc reload rather than the entire page you will need to implement some AJAX. I have answered a question on how to do this with Joomla components before, see here: how to use Jquery AJAX in Joomla Components?