I want to test each downstream of several clients (~100) which are connected to a media server. They are continuously downloading media files and I want to check which clients have a slow internet connection. Therefore I don't want to test them manually by hand again and again. So is there a way to log and monitor the download speed e.g. through apache?
You best bet is to log this information at your firewall if you can. I know of a few firewalls (PFSense comes to mind) that will provide this information in a real-time graphical display (a breakdown of in/out speed per source/destination). It should be possible to log this information so that it can be parsed at a later date for analysis.
continuously downloading media files
e.g. through apache
...but apache is not a streaming server.
But leaving that aside, what's wrong with the standard apache logging mechanisms? (for preference using %I/%D rather than %b/%T, although in both cases you'll get a better answer using regression).