zero article before profession (estudiante)

Hola Richard

Both are correct, you can also omit it on the second sentence. Roger es estudiante también.

The presence of the article is justified with también because you are adding a bit more information to that second part, but to be honest, to me, it would sound a bit more natural to omit it in both sentences. 

There is no hard rule about when to add the article, it's a bit subjective. When there is a bit more specific information with added elements then the article tends to appear. 

In this very basic lesson we focused a bit more on when people introduce themselves to other people with more simple sentence, like, "Hola, me llamo Inma y soy profesora." - in this context then the use of the article would be really odd. 

Saludos

Saludos