Mjan,
I am no expert but here is what I did;
Through FTP I went to themes folder, selected the theme folder I am using, then modules and blocksearch... inside that folder there are two files (blocksearch-top.tpl and blocksearch.tpl). All i did was edit the blocksearch-top.tpl file as per explanations here;
http://www.prestashop.com/forums/topic/355246-solved-quick-search-block-module-provokes-unsecure-ssl/?p=1787175
From your page it also looks like the facebook like add-on is also causing the problem as well as the search block.