In Brazil, I've never heard anyone ever use "traje" for costume — it's a mans suit. "Costume" is also correct.
We use that in some situation. For example:
Traje(s) típico(s) = Folk/regional costume
Traje de gala = evening dress (a formal dress)
Traje de banho = swimwear.
Chofer is wrong?
Do you mean "chauffeur"
why can't the driver be female and it be da motorist?
"o motorista (male)" or "a motorista (female)", the word "motorista" can be the both way. So, your answer should be correct
At least where I'm from, we'd call this a "uniform", not a "costume." "Costume" is used mainly to talk about what you might wear on Halloween ("fancy dress," for those of you in the UK), and sometimes to talk about traditional dress.