I have to admit I don't hear people say this sentence very often, does "Nie mam zawodu" mean more along the lines of "I don't have a job at the minute/I'm unemployed," or, "I do odd jobs, I don't have a specific profession"?
The programme does not accept "trade" here, offering only "profession" as a correct answer. What is the better word for "trade" (such as a joiner or electrician) and what is the equivalent word for "occupation" (as in what is your occupation?" when someone asks what you do for a living?)