Please read these to learn about metabolism, fat burning, proper foods to eat, macro and micro nutrients, etc:
They are really excellent resources. I do disagree in terms of the meal frequency they recommend in those articles (I believe more recent science indicates you can eat less often and be fine).
A more recent article on meal frequency on ABC leans in this direction of eating less often:
OJ and Banana isn't ideal, it's almost all carbs/sugar. If you are going to eat, have some protein with the meal as well, otherwise, just skipping breakfast would actually be more ideal.
Regarding the lunch, once you read the article I linked to, you will understand healthy food choices and you can either select something healthy or pack you own. My son is in school and yes, there is the typical junk and pizza available, but there is always a more "normal" option such as chicken and potatoes or the salad line. Make sure you've explored all your options before writing all the food off as terrible.
With the above schedule, what can I do to loose fat weight? What should I eat/not eat? Anything that you guys like to eat for breakfast/Dinner? What is good for a sack lunch? I am allergic to peanut butter.
That schedule will not interfere with fat loss in any way. Fat loss is accomplished through eating well, training hard with weights and getting sleep. You asked for food suggestions, but it really doesn't matter what anyone on ABC likes. Read those articles, find out what is healthy that you also enjoy, and eat those foods. There are plenty of cheap, healthy and easy options out there.
You could not be making a bigger mistake.
I'm not planning on doing strength training as I am plenty strong for my liking, I will do mainly core training and cardio with a bit of arm training (my legs are already HUGE, muscle wise).
As I wrote in response to your other thread, your body doesn't care how it loses weight. If you are in a caloric deficit, your body wants to shed fat and muscle, it has no preference. You have to eat wisely and train hard to give your body a reason to keep the muscle and shed fat instead.
Trust me, to achieve your goals, you will need to keep strength training.
Also, any workouts/workout systems that I might not know of feel free to inform me of.
You mentioned in your other post that you are doing the "13 week fat burning diet". My advice is to finish the program. The only way you will ever know how/if programs work for you is by completing them as the author intended.
Afterwards, there are many great programs you can run while on your fat loss journey:
Starting Strength (or any 3x5 or 5x5 derivative there of)
Layne Norton's PHAT
The program doesn't matter so much, as long as it isn't completely idiotic and as long as there is some heavy lifting involved to give your muscles a proper stimulus.
Fat loss is achieved with diet, NOT with core training and cardio. Muscle preservation is achieved with heavy training, NOT with core training and cardio.
Can you do some cardio? Sure, but it is secondary to eating properly and lifting hard.