In masthead.php, instead of adding the animation classes to <div class="hgroup full-container">, I added them to <header id="masthead" class="site-header" role="banner">, this seems to take care of animating menu along-with the header.
Regarding the Submenu disappearing, somehow the submenu was rendering behind the slideshow. Setting up of z-index helped solved this.
I have added the following rules to Settings > Animate It! > Custom CSS
Please let me know if this works as per your requirement.