Is it the personal pronoun necessary?
It is only used for emphasis.
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.
is the word order rigid here? Could I say "te olvasod az újakat?"?
Yes, that's a possible word order. It changes the emphasis, though: more like, "Is it YOU who is reading the new ones?"
What about "Olvasod az újakat?" It didn't accept that.
It's fine. The focus shifts from what you're reading to what you're doing with the new ones.
Is this okay for you-plural? "Olvassátok az újakat?"
Yes, very good. :)
What's wrong with olvasjátok az újakat?
Sorry! Should have read the posts first. Please ignore
Why isn't this accepted?
Ti olvassátok az újakat
Kwhalen, there's no particular reason for that. It's also a fine translation.