does not "saat kaçta" mean "AT what time" in English?
Yes, the "at" is optional.
Why is not corect "at what hour are we going?" Here it is not supposed to indicate the exact hour not just the moment/time like "zaman"?
That should be acceptable. They may have left it out because it is not very common in contemporary American English.
As is often the case, the last syllable of the recoding is frequently inaudible. In this case I heard “gidiyor”, not “gidiyorUZ”. “GidiyorUM” is also difficult to discern.
Apparently this was reported 2 years ago and has not been addressed.
At what time are we going IS very common in English English, it should not be marked wrong.