Shouldn't it be розмовляти?
Yes. At least it should be accepted as well.
In the Tips Notes it says that говорю means I carry. Is this a typo or just a weird word?
Edit: they messed up the second conjugation table
That's a mistake
Why do you use the instrumental case for this and not the accusative?
Because instrumental answers the question often of how. Im writing with a pen im eating breakfast with porridge im speaking with a language.
In english it makes little sense