As I wasn't able to solve the problem related to JOdin3, I rooted the device using heimdall and CF-Autoroot. It worked flawlessly. I installed Clockwork Recovery and I'm able to backup the system. Now, I can continue upgrading the system to CM 12.1. Anyway, heimdall-frontend seems to be more advanced than Odin.
Here's a tutorial for it: http://www.all-things-android.com/content/how-root-samsung-mobile-device
The tutorial shows how to use CF-autoroot by using the heimdall-frontend. First, you need to download/create the PIT file from your mobile phone. Be aware, that there is no finished dialog or something similar shown. After doing this, you can flash the recovery image and the cache image from CF-autoroot. If everything went fine, you should see "Flash completed successfully"!
I installed CM 12.1 successfully and Android 5.1.1 is now running on my I9300. :)