Ask them the IP address of hosting server, then you can use ftp for downloading files, images. For WordPress content, you will need to access to database tool, such as phpMyAdmin. Ask them too.
I saw this kind of issue with a plugin, not WordPress itself. But you can try to turn off plugins, and switch to the default theme to see if it’s happening again?
Not sure. I see you have a WordPress installation at https://frameda.fi/htdocs/ but it’s not working correctly, cause it should be installed at https://frameda.fi/wordpress/. That’s why I am asking you to upload again to show exactly the error.
CSS is not loaded, the page is not fully loaded either. So, I guess something wrong with your code, if you are using customized backend. Or your site is embedded external components, that external source is not working anymore.