He is a speaker and writer
He is an architect and a dancer
When the two things are related, it is possible to leave out the second "a" in the sentence.
When they are a new idea, it is not.
So for your example, it should read: he is an old, tall Brazilian and a student
Because the student is a new idea
However, in the following example:
He is a proud, hardworking Brazilian father and student
here student is not a new idea, and so it is more like a list where you do not have to repeat the a
He took a kettle, bottle of milk and jar of coffee into the sitting room.
This is a list and "a" doesn't need to be repeated
He took a kettle and an orange into the living room and then took a book and a cat back into the kitchen - where they are not logically related and it makes more sense to put a/an