After some good assistance through mail, @cyberdave and I managed to narrow down the solution:
There were two problems:
1. I needed to rename fonts and re-upload them. That fixed the fonts-issue.
2. The images export didn't go well either. This was the problem & solution:
I used a SVG in the favicon & webclip uploader. That worked on the screen but stalled the export. Obviously I didn't read the caption about the supported file-types there. So I made a new favicon and webclip with exactly the right size in Photoshop and saved them as PNG. I used them for favicon and webclip and that allowed me to export.
Thanks to @cyberdave for his support.