"Are you reading the new ones?"
Translation:Te az újakat olvasod?
No, "Az újakat olvasod?" is also correct, and it's more commonly used in everyday life.
This personal pronoun being included or NOT is a real problem on more that a few of these questions, and it's very frustrating having to guess which is required each time.
Yes, that's a possible word order. It changes the emphasis, though: more like, "Is it YOU who is reading the new ones?"
It's fine. The focus shifts from what you're reading to what you're doing with the new ones.