Can you tell me if the belt in my driver's side front tire is broken?

What is your question?

My daughter has a 2002 Ford Focus hatchback. The car thumps a little bit when driving, but you can mostly feel it through the brake pedal. My wife describes as if the car has square wheels. My daughter often hits potholes pretty hard. The tire is a Goodyear Eagle GT. There is a very fine hairline crack for about 1/3 of the tire on the sidewall close to the tread. I don't think it's wheel balance - just doesn't feel like that to me. I'm thinking the tire belt may be damaged. I have 2 questions: (1) does my diagnosis sound correct and (2)is the tire safe or should it be replaced?