I tried just setting the widget to ‘custom query’ and entering this in the input below ‘custom query’ (where 35403 is the ID of a page):
That works for me, so I’m guessing the AJAX issue is something specific to your site. Try deactivating all ofyour other plugins and switching to the 2012 theme to rule out the most common sources of AJAX errors. Some other suggestions are here:
If that doesn’t help, please send a URL and a login to your blog (use the contact form) and I’ll see if I can spot the problem.
I’ve never tried the add_filter approach myself but the padding sounds like a CSS problem. As an alternative, you could use do_shortcode() directly into the template’s sidebar.php file.