So, can you go here:
and log-in as the admin?
If you can, that is how you access everything at your site. It’s the engine that runs it.
The whole idea of a CMS like Joomla is that you do not need to use FTP or play around with any of the php at your site. You use the Joomla administrative backend to add your images, edit content, add new content, create menus and other navigation, install or change your template, add components, pretty much everything.
All your website content (the text, your articles, stuff you write, site settings, users, all that kind of stuff) is then saved by Joomla into the database (but you always access it/edit it from the administrator backend).
Your images, which you upload via the back-end editor, usually, are most likely in a directory called ‘images’ and then in a sub-directory of that called ‘stories’ - it may be customized differently, but the images ARE in the web readable area of your site (where all the php files are).
Looks like your site is using a custom template and probably a gallery component. Once you log-in, it should make a bit more sense.
In normal practice you shouldn’t need to access the database (unless you do NOT have admin access to the site at all because you’d need to fix that and that’s where you could reset the password).
Go to http://docs.joomla.org/ for lots of info about getting started with your site. Once you get in, look at the components and see what is creating your gallery. You can probably go to that developer’s site to find out more about how it works.