If the sentence was "I ask her a question" would the translation be
אני שואל אותה שאלה?
And couldnt this also mean "I ask the same question?" I think this might be the question that the guy was asking.
Yes, I suppose. Like when it is not clear who of the class is being asked by the teacher and they ask אֶת מִי אַתָּה שׁוֹאֵל אֶת הַשְּׁאֵלָה הַזָּאת whom do you ask this question?. But the inner object שְׁאֵלָה can usually be left out anyway.