Here is some information that could be useful to you:
1) The current [latest] version of RadTooltip has automatic browser boundaries detection and moves the tooltip away from the browser edges - it is displayed fully visible on the page.
3) In case you *are not* OnAjaxUpdate to fetch images, this taks is very simple - becasue once an image is fetched by the browser, it is cached. So, each subsequent request to show the same image does not cause the browser to make a request to the server, rather it loads it from the browser cache. So, there is no need to write any specific code that tracks which images are loaded.
All the best,
the Telerik team