The best book that I found helpful is Edexcels Mathematics Textbooks. Along with the solution banks.
I find that book so much better than any other book tbh. You start from the basics, and the examples provide great step by step solutions and once you get to the exercises for each topic, they make sure you know it from the basics to the most hardest questions. Its in varying difficulty, where difficulty goes from easy to the hardest once you progress. Including exam past paper questions
And the great thing about that is that they have answer booklets that have step by step solutions for every single question in the textbook(Solution bank)
This is a book designed to give you the best way to actually apply what you learn in doing questions.
If you want a history on mathematics and how they are created then I am not sure, someone else can help you with that.
1. * What do you believe is the best / proper way to study math?
For this question also the textbook really helps. Do all the exercises and use what you learned to apply logic and solve them. If you find a question difficult then check the solution bank for the step by step solution so that you can understand.
I would say doing exercises is the best way to learn
2. * What are some common mistakes people do when trying to learn math?
Mostly algebra mistakes regarding signs and such as addition and subtraction