Can we also say 你看新闻了吗？
You can definitely also say that. That is the word order that the Pimsleur Mandarin course teaches and it is a very natural and correct word order.
You can definitely also say that. As a matter of fact, that word order is the word order that the Pimsleur Mandarin course teaches. They say it is very natural to ask 了吗。
I believe "你看不看了新聞？" should also be accepted.
No one would ever say 你看了新闻吗. That is not proper sentence order. 你看新闻了吗 is the correct way.
This course is ridiculously wrong at every level. Unsubbed. SAD!