Thanks for respond, but I am not laying :) All I did to the code of WP Image Tooltip is just changed the class plugin should look for from "tooltip" to "cboxElement". I changed this part of Image-tooltip.php file:
open: 'fadeIn', // can be 'show' or 'slideDown' or 'fadeIn'
//height:'" . $imagetooltip_size . "',
//width:'" . $imagetooltip_size . "',
It's just variables. I had to look for "cboxElement" class because plugin "jquery Colorbox" automatically adds this class to post images and so I don't need to add another class like "tooltip" manually. I modified css file of plugin "WS Image Tooltips" too, using correct syntax.
As I mentioned before, these changes were tested and worked in Chrome, Firefox, even Internet Explorer. And even using proxy with browser caches deleted (to be sure that i am just a random guest for my site). After BP install, tooltips began to not to show correctly. Firstly, I didn't see that strange string in image url, so I re-installed "WP Image Tooltip". But problem still exists. Maybe I could try to comment some lines in BP security created .htaccess file, because where are lot of lines with Rewrite rules. I am just not a specialist, to know what lines or what code could make that strange strong appear. Thank you for your time.