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The calorie estimations should be within 10% IF you are honest about your activity level. The average person needs about 2,300 calories per day, which means the calculator could be off by as much as 230 calories. Over the course of 1 month, this is equal to ~7,000 calories (2lbs). Most people, however, overestimate how much they work out (ie they choose 'Heavy Exercise' when they should choose 'Light Exercise'). You should use the TDEE calculator as a reasonable estimate to start with, and adjust your calories up or down based on your weight change over time.
You're eating too many calories. If you were eating at a sufficient deficit, you would have lost weight. Be aware that losing weight takes time, so be patient and pay attention to how many calories you are eating per day - and decrease your daily calories if you haven't lost any weight for 4 weeks. It's also true that your weight loss can stall. When your weight stalls, I've personally found the most effective course of action is to fast for 2-3 days. When you fast for a few days, your body will finally "let go" of those lbs.
The Body Mass Index (BMI) formula is based on average weight for your height. People come in all shapes and sizes, think about the football players at your school growing up. Some of them are not especially tall, yet they weigh more because they have lots of muscle. BMI has frustrated weight lifters for many years. Just understand that the more muscle you have, the more that the BMI scale with skew high.
There is no "best" macronutrient ratio, but what's important is that you eat enough Protein and get the vitamins and minerals that your body needs from real, whole foods. My opinion of the perfect diet would probably be: Steamed Veggies with Beans, Chicken, Fish and Fruits.
For most people, at least 1 of the formulas should be reasonably accurate. Just like with BMI, the more muscle you have compared to the average person, the less accurate it will be.