I'm not sure what you mean with the porftolio image issue. Can you give me an example/screenshot. There are a lot of plugins running in conjunction on the site linked so I'm not quite sure what is supposed to work/look and what is responsible for it (ie, it could be a plugin or the theme or something custom you have already done).
Yes, you can customize the layout of the search results. You'll need to modify the php file called loop-search.php located within the includes folder. You can also use something like Firebug to inspect the individual elements on the search page and then add/change those attributes through the custom.css file.
As far as I know, you can't easily train your search to display categories based on the search terms. What you can do, is create a menu link to display any category you have created for your portfolio items. You can do this in Appearance>Menus.