Will doing 500 sit-ups and 1000 push-ups a week along with diet, weightlifting, and walking be enough to drop weight? or should it be more intense?

More or less: More cardio, less push-ups and sit-ups. If you are obese, consider walking in a pool, stationary bicycle, things that get your heart rate up without pounding your back or large joints. I would start with 5 minutes/day. Add 5 minutes per day, as tolerated, till 30 mins/day. Maintain that for at least one week. Then, again increase that 5 mins/day till desired end result. Ask doctor to help guide u.