Problem with image uploads – take up file size in FTP – (not) showing randomly

Dear readers,

I have a problem I can’t fix for a client of mine. I did search for 4-5 hours, and if the answers seems simple, I’m sorry but I really did my best effort to fix this myself.

The website I’m talking about is this one.
It wasn’t made by me but I had to make some improvements over the last designer.

The problem
The site contains images uploaded to the media library. Now none are visible, while last time some were visible. The images (ranging between 50 kb and 4 mb) are uploaded to the FTP server, taking up actual space, and in the ftp server I can view the images. BUT they are not visible in the media library.

They do upload, but they don’t show any visbility. I don’t get any errors. See the next image for an example:

image of the media library in WP

Now I disabled all plugins, changed the theme, did the same procedures, and they all led to the same problem. Now what I don’t understand is that two days ago, I did see some images on the actual website… I know I tried some file permissions to the upload folder (744/755/777 even), but shouldn’t that help the problem instead of making it worse??

The strange thing is, that the website is located in a webspace/siteapps/wordpress-35751 folder on the FTP. I have never seen this before.

I’m sorry for the long, confusing message.. I just don’t know what to do anymore. I hope someone can help me!

Thanks in advance ??