See my previous post, "FO3: Age 16 and the infamous GOAT", for more details on this section of Fallout 3. There's a few choices you can make on the way to the exam (I show one of the "good" choices), so save early in this section so that you can replay it.

As for the GOAT, there's really no right/wrong answers, and you can change the 3 skills that get picked after handing in your answers.