The Theoretical Minimum lecture series on theoretical physics by Leonard Susskind. Covers the basics in a very approachable way. I wish this had been available when I studied physics.
When I was in school "scientific method" wasn’t teached as a separate topic, but more like the result of "osmosis": you are given many examples of how science works and you somehow learn by this the process of science itself. Ok, you are taught how do do proofs in maths and how to do experiments, but no direct reference to a concept like the scientific method.
An (maybe) interesting fact is, that in Germany the notion „scientific method“, to my knowledge, is largely unknown. For example, there is no link in the english wikipedia entry you have given to the german wikipedia. When I studied physics in Germany no one ever used that term.
There is a free PDF on the nature site, but the paper is also available on arxiv (https://arxiv.org/abs/1407.4437), the first version on the arxiv dates back to 2014. It's strange, but I find the arxiv version much more readable in terms of typesetting than the polished version in nature. Also there are additional appendices in the arxiv version.
I do not know "Mathematics: From the birth of numbers" but judging from the Amazon quick view it seems to cover a lot of ground (BTW: one thing I missed in my list are the basics of differential equations).
Over 1000 pages is quite a long read, though. I never managed to read a (science) book as big as that from cover to cover myself. One thing I learned through the years is to never use only one book for learning. Books have different styles and not every style fits to every student. Additionally one book might be good at one specific topic and weak on another. So nowadays I always use a couple of books (or online resources) to learn a new topic.
Math is wide and deep. You won’t need to cover every topic in math to get going with physics. If you really are interested in physics there are many things in math, which are, well, less important (for doing basic physics). For example LCM, GCD and factoring. I guess, these things are somewhat important in Computer Science, but I never encountered them in a physics problem.
So to get started with physics, I would suggest that you focus mainly on analysis (differentiation and integration) and vector algebra. As an addition maybe the basics of complex numbers. This can be learned relatively quickly.
With these you should be able to follow the Feynman lectures or watch the very fine „Theoretical Minimum“ series by Susskind (http://theoreticalminimum.com)