Question: Is doing a long period of cardio good enough to lose weight?
Answer: Doing cardio will help you lose weight as long as you are burning more calories than you are taking in. It is a great way to start but you will get better results by adding in some weight training exercise with your cardio. I would do 30 minutes of weight training with 30 minutes of cardio.
Question: I'm looking for a good core exercise that will also strengthen the back - any suggestions?
Answer: Working the core in general will strengthen your back. I would recommend doing your sit-ups on a stability ball. It will help you work your mid section, including your obliques, and will help you strengthen your back as well. You can also do planks for your mid-section, which will strengthen your core.