Can I really trust my food tracker??

I second delicious_croc.

1200 calories and then eating back any exercise calories would be the bare minimum a female should eat. If you don't eat back exercise calories on top of a 1200 target a day, you're actually more apt to see your weight loss stall quickly as your body conserves those calories in starvation mode. Eat back exercise calories all the way. You'll still be getting benefits of exercising (metabolism boost, overall health benefits, toning) but maintaining the right amount of energy for your body to function correctly.

You have to gauge your body. Everyone is different. MFP overestimates calories burned., I also think the cardio machines do too. So, I never eat all of my calories back, mostly stuck to 1200 calories. I just wanted to lose weight faster.

You are right to be cautious about the exercise calories. They're a guesstimate. If you are slightly underestimating calories eaten and slightly overestimating exercise calories burned, then you can actually gain weight or just make no progress when you think you've been sticking to the program. Many people don't eat back exercise calories at all, eat a percentage of them back (50%, 75%, whatever), or "bank" them and take a cheat day once a week or every other week. Anyone who tells you there is only one "right" way to do this is probably full of it.

Pay attention to your body. Weigh yourself once a week to gauge progress. If you're staying the same, cut down your calories a bit or increase your exercise. If you're gaining, then definitely cut down your calories and maybe exercise more too. If you're losing 1-2 pounds a week, keep doing what you're doing! We can all say what has worked for us, but that's no guarantee that it will work for you exactly the same way.

My best advice: buy a digital food scale. You would be surprised by how imprecise measuring cups and spoons are.

Best of luck on your journey!

PLEASE ignore this advice. DO NOT go under 1200 calories -- that is dangerous, unsafe, and will only result in future problems! If anything, get more detailed. You can use several sites (including this one) to calculate your BMR (basal metabolic rate) or your TDEE and go from there. If anything, up your calories some. Then good a good food scale. You would be surprised how off you can be with certain foods -- pb is a prime example! I even used this example on another site. Peanut butter servings are 2TBSP, but you wouldn't believe how often people 'eyeball' only to discover later that they were actually eating closer to 4TBSP... that's a difference of almost 200 cals! So, when it comes to fats like oil, pb, butter, etc., you need to be sure and measure that. Another thing you can do is get an HRM (heart rate monitor) to wear during workouts. That will give you the best numbers to plug in. Then eat back those cals because even if you go up to say, 1400 cals, baring any medical issues, you should still be losing. Wouldn't you rather work it down slowly and have wiggle room? Options? A better chance at long term success? I'm sure you will get lots of advice and info on here that's even better than mine, but these are the two best options I think you can have if you are really worried about the numbers.

One last thing, if you are worried about the food entries, just try comparing the packages for a few weeks until you build up your food entries to what you typically eat. I've only found a few items to be inaccurate. If you are eating mostly lean meats, fruits and veggies, you're probably darn safe unless you are eating huge portions.

I'd say to buy a heart rate monitor, you wear it while you exercise and it can be a better reading of how many calories you burn.

What is my TDEE??

Total Daily Energy Expenditure, which is the sum of your RMR (Resting Metabolic Rate, the number of calories you would burn lying on the bed just breathing) and calories burned from physical activity - not just exercise, but everything else you do, from cooking to standing to walking from place to place. One decent calculator for *estimating* TDEE is:
http://scoobysworkshop.com/accurate-calorie-calculator/

To go back to the original question: you should eat the calories you *actually* consume during exercise, if you're using MFP as it's designed. However, most estimates of calories consumed by exercise are exaggerated. (MFP tells me I burn nearly 900 calories in an hour of cycling at 15 mph; the reality is more like 550-600 on flat terrain.) I would suggest starting by eating 65-70% of estimated exercise calories. Compare your progress after a few weeks against your goals, and adjust as necessary: if you're losing too fast, eat back more; if you're losing too slowly, eat back less.