Yes, you are correct in your assumptions. Because your body fat is low the calculator assesses that that your body weight must be appropriate which it is not. You are underweight. Therefore, no matter what your weight, if you maintain 8% body fat, the calculator will tell you, your body weight is healthy. I have fixed that exception. Usually persons with low body fat and high body weight have problems with these types of calculations. You are the exception with low body fat and low body weight.
The healthy body weight range of 144 – 176 assumes a body fat of less than 25. Of course, you could weight more than 176 if your body fat was low.
A doctor or a dietitian can assess your weight to height ratio. You are underweight.
Counting calories is boring. It is easier to write down everything you eat and then use nutrition analysis software to keep track of calories, grams of fat and other nutrients. It has over 18,000 foods to choose from and there are a lot of “entrees” listed and many fast food restaurants. Don’t know of a good book for calorie counting.