1) Cost depends on how many people are flying. For 4-5 people, it is far cheaper to drive. Flying a family of five is around $3000 on JetBlue depending on the season. Driving you have the cost of gas, meals and hotel (optional).
Gas costs depend completely on your vehicle. My toyota sienna (fully gassed up in NY) required only two stops for gas. One in Virginia, another in South Carolina. Figure around $200 for gas each way.
Hotel room if you don't want to drive non-stop is around $140 for a moderate chain hotel in South Carolina.
For meals we stopped for lunch at Chick-Fil-A and had dinner at Cracker Barrel, both cheap. Driving, on average, will be less than 1/3 the cost of flying.
2) It does not take 24 hours to drive from NYC to Orlando. It's about 16 hours total driving time. You need to leave NYC at around 3-4am to avoid traffic hotspots around DC and Richmond. If you are leaving on a weekend, traffic will be minimal unless there's some kind of major accident or major construction.
3) If you want to split the trip up, stopping in mid to southern South Carolina on the first day is a good idea. That's about 10 hours. You can get a hotel room in a nice chain hotel for around $140.