Not really, in English you don't use articles if you're talking about a non-specific case. No one would ever say "the breakfast", for example, unless you were talking about one specific meal you ate, one time. For example, "The dinner my mom cooked last night was great"
i wrote "i drink the coffee after the dinner" it's not right but in the correction is the same !!
Did the correction have "the dinner" or just "dinner"? Because in the context of the sentence given, it is "dinner".
Why is "I drink the coffee after the dinner" wrong? "du cafe" i.e. "de le cafe" should translate to "the coffee". Shouldn't it at least be marked as correct?
You added "the" before dinner. That is where you might have been wrong, since it is more normal to just say "dinner".
And no, du cafe is neither de la cafe (de le cafe, it is) nor it means the cafe (that would be le cafe)