We'd have no clue how a 3rd party plugin will impact your site or the Framework as I'm unfamiliar with the plugin. There are many elements of your site which use lists. If there are conflicts, you may expect it to affect the menu or other areas. This is why I recommend using custom CSS. At least you know exactly where it will be applied.
I couldn't tell you where to apply the shortcode. They may be applied in a wide range of areas, depending on what they do, how the lists are to look, etc. If you want the list in a page or post, add the shortcode in the edit area. If it's to be on a blog page, then yes, a content box is more applicable, provided it's a static blog page.