For learners familiar with German: Notice the similarity to "Erwerb", as in "Broterwerb". :)
Is this German word an explanation for the ethymology of the Danish word erhvervet? Does et erhverv exist?
1- Yes, "erhverv" comes from "erwerb".
2- Yes, being a baker for ex. is "et erhverv".
I didn't heat the t at the end. Even when listening back I can't heat it. Is it supposed to be silent?
The sound bite is not so good. It is supposed to end with a [əð] pronunciation in the sound bit. You can also pronounce it with a [ət] ending, but it is more normal to hear the soft d in the end. This goes for a lot of words ending with -et.
Listen to this sound bit for example which is a little better: http://www.forvo.com/search/huset/da/
Try Welsh. I have the hardest time with some of those words. I figure that just practice, practice, practice, and we'll get it.