Angel is correct. 'Them' refers to answers, so you can't change it as you suggested, as then your 'them' would refer to the questions, not the answers. It also isn't natural to concatenate broadly and generally like that.
You could use: "How do you answer very specific questions and use those answers broadly, and generally?"
'take answers to very specific questions' is like a condensed version of 'take answers that are answers to very specific questions'.
Also note that there are a couple of errors in your original too. It should be "broad, generalized", with the space after the comma, and a D on generalized.