Go to a link ?? Where inside the Dialog ?? If yes, instead the $(this).dialog("close"); use something with the location.replace() method of plain Javascript [Don't know now if jQuery has something to that], if not, do the same but for the window and close the dialog. Or make an anchor with target _blank. Be more specific, please on what you need.
For the first question, is easy; give the form an ID, and then instead the $(this).dialog("close"); in the "Save" button, use ("#FormID").submit(); just as simple as that. But you probably need to do the submit via AJAX, for what you'll need to assign a custom event handler to that submit ...
Ah ! If some line of code says ignore! You should do it !!! take it away, unless is necesary
Cheers