Take it easy. It's a goodwill of developers or users to write something here (even they guessed the problem).
For you question:
Good way to debug any request (whether it ajax or not) with use of modern IDE (Eclipse, PHPStorm, NetBeans) and any PHP debugger, like xDebug or ZendDebug. It requires some effort to set it up first, but it save time later just setting up breakpoint and get all info and line-by-line execution.
Both of urls must work:
As Alex wrote first variant consider «ajax helpers» use, and in normal flow this link must works fine.
When you run
admin/config#get;n=edit&o=plug&p=html then browser loads common
admin/config page then ajaxhelper script (resides in "js/base.js") get hashed-string
get;n=edit&o=plug&p=html and then via ajax loads up page with these parameters into main block. That's how it works.
So first of all check your .htaccess (if you use apache) file to conform actual "sef-urls.htaccess" example file. And check "js/base.js" load Ok.