Translation:You read a book and I read the newspaper.
I strongly recommend the re-doing of the portuguese audio. Many sentences are garbled, characterless and/or nearly incomprehensible. I feel the quality is lower than the other languages I've tried. I had to click the slow down button in order to make out the 'and (e)' and the difference between the 'a (um)' and 'the (o)', which was nonexistent in the normal speed audio. If a portuguese native speaker such as myself and other commenters here couldn't understand your audio, it's a sign that maybe you should consider revising it. Best Wishes
"Jornal" can be either printed, radio or television news. So, to your question: yes, and I believe it is even better translated that way!
Just don't confuse "jornal" with "notícia". "Jornal" is the mean of communicating the news (a newspaper, a TV program), and "notícia" is the news itself (the information).
I don't know if this is a regional idiom, but I would never say "I read a newspaper;" it's always "the newspaper," "the paper," or "the news." The only exception I can think of is if there is an adjective or descriptive clause, such as in "I'm reading an old newspaper" or "I'm reading a paper that I bought on the way to work." But, like I said, this might be somewhat regional.