It’s a bit hard to give you accurate answers as it looks like you have some custom css going on :)
But..normally with other wootheme themes there is an option to turn off the pagination buttons underneath the slider in the theme option in slider settings.
Re the space below the navigation buttons. It might be that the size of the logo is causing this. The theme is designed to have a smaller logo that fits to the left of the nav. Because you have a full width logo this is causing the gap.
Re smaller slider. Normally there is an option to adjust the height of the slider in theme options. Is there an option for this?