I found a solution.
A proxy is connected upstream in my new provider hosting package (64Bit Hosting Domainfactory). But I only found out after searching.
That was the problem that files couldn't be downloaded.
In the solution it was written that you should put an entry at the beginning of the .htaccess file.
Header set Accept-Ranges none
RequestHeader unset Range
is it possible that the new version of JD also works without the entry in the .htaccess file?
I don't have that much idea what the entry does, but it works.