I think "sich wünschen" is more like hoping for it, like, "I hope to get the job". You still want the job but it has different Connotation
Why not "would like" instead of "wish"? They accepted that for wünschen on another problem.
Is this declaration of a wish for a particular job? Is it because of use of the definite article with "Beruf". "I wish to have a job" is not accepted, because it is general statement?
No, 'Beruf' means 'job' in the sense of 'occupation' (as in 'doctor' vs 'teacher'). You wouldn't use it if your applying for a particular job. In that case you'd rather say: "Ich will diese Stelle/diesen Posten/diesen Job".
That said, 'den Beruf' refers to a particular occupation ('doctor'). So, 'a job' is not a valid translation.
Which is really a better translation of "I want the job":
"Ich wünsche mir den Beruf"
"Ich will den Beruf haben"?
To me, the second is a more direct translation...
Why is here the reflexive pronoun in dative and in the previous exercise "sie wünscht sich mehr" in accusative?
I don't know if there's any logic to it (someone please correct me if I'm wrong), I think it's one of those we just have to learn. Here's a long list of which verbs take dative and which accusative (or both) http://www.pons.de/daten/pdf/Praxis-Grammatik/04_Verben_mit_Dativ-_und_Akkusativobjekt.pdf
Your sentence implies that you didn't get the job. You wish that you had the job already now. The German sentence also can apply to the future. My translation was: "I whish this profession for me" but it was not accepted. Maybe somebody can help me why?
I think it's a really weird thing to say in German anyway, and I'm not sure, how it would be translated best. Your translation is better than "I want the job" by far, because it reflects that you are neither talking about a single job, but a profession as a whole, nor just "wanting" but wishing for something..
Why not "I would like the job for me." ?? Doesn't the phrase imply a more personal desire than just wanting?
Ich will den Beruf = I want the job I wünsche mir den Beruf seems a bit less definite.....I am wishing the job is mine.
I want the job?? Ich wünsche mich das Stellenangebot/den Job, nicht "den Beruf" ! I want to learn a job/profession/a (particular) craft. Ich wünsche mich einen Beruf zu lernen/Ich wünsche mich das Fach zu lernen. The exercise here doesn't make sense, or we change the German sentence, or we modify the English.