Before Apple acquired Testflight, it was necessary to include all UDIDs of the beta testers in the distribution profile that was used for signing the app before it was submitted to Testflight.
With the new integrated Testflight environment in iTunes connect, do I still have to register the UDIDs of the testers or can I just invite them via eMail as external testers?
I have not used the "external testers" yet, only the internal ones. You do not need to know the UDID of the devices that will be used by the testers, only their email addresses. I also believe the user has to open the email directly on the device to trigger the initial TestFlight download inside the TestFlight application. Also, and this is kind of obvious, the "tester" needs to have the TestFlight app installed on his/her device.