The menu is under the logo because of your modifications. You do not use original theme files but the modified one. So the only thing you can do to move menu down is the following css:
@media only screen and (max-width: 767px) { #Top_bar .menu_wrapper { margin-top: 50px !important; } }
Comments
this is how sticky header on mobile works. If you don't like it, please turn off sticky menu on mobile under Theme options > Responsive section.