WordPress algorithm for looking for an image of a certain size has some condition checks which does not always result in finding the image of right size. I have had issues before with it. But in your case, I see an image of size 400×400 which is a loner since other images do not have a image with this size and theme does not support 400×400.
This can happen if you uploaded the image when the theme was not activated/installed. I think to clean up this whole thing, I would try running the –
http://wordpress.org/plugins/regenerate-thumbnails/
If that does not work, try this –
http://wordpress.org/plugins/force-regenerate-thumbnails/
Second query – possible with Javascript only. Again Google is your best friend here and hopefully something like this will help with click attached to those category links –
http://stackoverflow.com/questions/16765292/display-text-in-div-when-javascript-onclick