Hey Venutius, thanks for your questions regarding this plugin.
Unfortunately, I haven’t explored having the icons displayed conditionally from page to page yet, but that is a feature I have planned to add in the future. I’m not sure yet if this will included in the interface itself( most likely ), or if it will be something that is specified in the filter manually by a theme in the functions.php.
In terms of getting round containers and no icons, I’m not entirely sure what would be causing that. If you have a URL to the site where you have this happening, I’ll be happy to take a look at it. Since this plugin is relatively new, it hasn’t been tested across a wide range of themes.
I would assume if you have added some icons to a menu, have the menu assigned to a menu location, then it’s likely it could be a CSS conflict in the theme. I’ve ran into a couple of issues in my testing against some themes, and will be providing an update in this upcoming week to reset some of the styles found in menus, and override with the styles provided by this plugin if icons are assigned.