Translation:We are not professional.
yes, and the noun professional could be translated as "người chuyên nghiệp"
but if it's being used as an adjective, it needs to be modifying a noun. It's not, however, in this sentence. i.e. We are not professional actors; We are not professional athletes.
not correct. You can't have a professional "we." Professional was misused in the sentence we were given.
I don't see problems having someone being professional. yes, "professional" is an adjective here, but it acts as a predicative adjective not an attributive adjective to we.