In a lot of ways, hiking Mt. Whitney quickly is harder than running a marathon. Yet many people try to do it without any real training. The best way to attain the fitness to hike Mt. Whitney in a day is to hike a LOT. It is no fun to be at the summit and sick. As you scale up your hiking training, you will gain more confidence in attempting Whitney. Personally I wouldn't attempt Whitney based on what you posted until you've gotten your fitness to a point where you start to feel confident about your body's performance on the day.
I've never seen anyone using oxygen on Whitney and I don't think it's necessary. One thing you could do to ease the transition would be staying in Mammoth Lakes or somewhere high up for several days prior to your attempt.
On fuel, I try to eat a lot the day before, but not stuffing myself. I eat a lot of calorie dense foods both before and during the hike. I try to avoid gimmicky things like gels and focus on real food. My favorite thing is ordering a full sized pizza the night before a big day, and then eating the leftovers during the hike.
