I can't give you much advice from this point other than to ask the people who made your gallery scripts and such to give you a fresh copy so that you can delete the site and start over. You can dispute the charge with your credit card company if they won't play ball. At least ask them for more detailed information such as how does the gallery work. What sort of database is utilized when storing the information such as logins and passwords, if they are encrypted or not (or do you know already?). If you can't find out how to fix the logins that are having an issue you should just delete the problematic accounts and create new ones. It won't stop them from being compromised again but at least it would be a temporary solution. The hard part is going to be finding out just how your files were compromised and how to patch it if possible. Otherwise you would have to pay someone to troubleshoot your site for you and that can be expensive since none of us likes to work for free. Only other option would be to use different software for your gallery. Something that you know how to install and maintain yourself.
As far as where to go from there I recommend you learn at least the basics of web design. Can't really find out what's wrong if you don't understand the language and how to actually make web pages and such yourself. There are all sorts of resources on the web for things like html, php, ajax, etc (the webmonkey is your friend). What if you wanted to change the color scheme or things like that, did they provide the files you could edit or tell you what you would have to alter? You have to think about that sort of thing unless you want your website to look the same forever. Hope you didn't pay too much for what you got considering they aren't willing to support you at all.