Designing a brushless DC motor:
You can't "reverse engineer" something that was not engineered in the first place. From an engineering point of view, there is nothing of value here. This is a nice demonstration of how to make a motor that works using inexpensive and easily-obtained parts. You can learn something from it, but it is not a good basis for an engineered motor design.

The major flaw in the design is the lack of any effort to design a magnetic circuit. A good motor needs a closed path for magnetic flux through good magnetic materials with an air gap that is as short as possible. You can inexpensively buy used text books that were published 15 or 20 years ago and find on-line engineering course material that will provide a lot more engineering design information that anyone here is likely to post.