Upvote:7
Did the Nazis ever have anything like prime time broadcast news?
No, there were no daily news broadcasts. What was shown was the, film based, Wochenschau (weekly newreels) that was also shown in the cinemas.
And if so, is there any archival footage of it?
No, the recording technology didn't exist to record the television camera input directly.
Most of what you see today, was filmed using a film camera and then broadcast.
All broadcasts that were done directly are considered to be lost.
The 11 minute 1935 documentary (see YouTube link below) gives you a good idea how things were done. The documentary itsself was first shown in the weekly newreels in 1935. It also shows how the, later, public video telephone service worked.
See also: What time of day was Hitler's opening speech of the 1936 Summer Olympics? - History Stack Exchange. The answer is based on the timetable of the television broadcaster.
Sources (German only):