Hi there,
Regarding to slider can you make sure you had added the custom template provided by themes. If not please
have a look on the tutorial here https://www.styledthemes.com/documentation/pro-themes/flat-responsive-pro/ This may solve your wired looking mobile issue. You can find uses of widget kit menu on left
And regarding to space at bottom please add this css on child theme style.css or additional section of customizer so your changes will not lost on theme update.
#fr-banner {
height: auto !important;
}
Updating the premium theme won’t effect on child theme.
Thanks