If my father needed a bypass when he was 55 years old, will I also develop heart problems while I'm still young?

Not necessarily. There is a strong connection of heart disease in first degree relatives but there are many other factors involved! Your best bet is to talk to your doctor and work on life style modification to minimize your risk of heart disease. Ie smoking, exercise, diet, are some of the things you can do something about. You can't change your family history. Start working with your doctor early for best result.
Possible. It certainly increases likelihood. The key is to discuss this with your pcp. If modifiable factors are identified and changed then your chances should improve.