To achieve the click image to advance to next slide functionality will take some custom JavaScript coding using owl carousel events: https://owlcarousel2.github.io/OwlCarousel2/docs/api-events.html
So something like the following JS Code should hopefully work:
<script>
var owl = jQuery('#SLIDER_ID');
jQuery('#SLIDER_ID').click(function() {
owl.trigger('next.owl.carousel');
})
</script>
(NOTE: replace ‘#SLIDER_ID’ with the CSS ID of your slider)
To get the “Fade” effect, select “Fade” for “Slide Transition” – the number of sliders for ALL resolutions must be set to “1” (mobile, tablet, desktop).
To display the slider thumbnail image links below the slider as per the example link you provided (yes, I did look), you will have to upgrade to PRO (that feature is not in the FREE version).