Blue ? Icon and big space on iPhone only

I think this symbol appears when an image or file cannot be found.

Edit : now i have inspected your page with dev tools – my pages with full-width easyslider and video inside as list item – looks totaly different to your DOM.

I got this <div id="mep_0" … container inside <div data-rel="slideshow-1" class="avia-slide-wrap " ….with all the video instructions inside

Ah ok : this seems to be a matter if the inserted url is a relative url and not an absolute url.
by the way it seem to be the only way to show the video on iPhones by relative urls – but than a message is shown : av-fallback-message if there is no fallback image.

so try: let there be the relative url to your video – do not enter a fallback image and:

#top .av-fallback-message,
#top .av-fallback-message + img {
  display: none !important;
}

or if you do not like to use the Sibling Combinator :

#top .av-fallback-message {
  display: none !important;
}
.avia-slideshow li img[src*="undefined"] {
  display: none !important;
}

ok – but it will work as i described above if you use relative url to your video – and do not enter a fallback image.
Then the css.