I watched a DIY video recently on building a brushless DC motor. Can someone demonstrate for me how to calculate the max torque & max rpm of that motor based on the components that are used in the video--not by using a dynamometer or any other device to measure the mechanical power/torque or rpm of such a device? There must be some EE method/s to reverse engineer & use such data to redesign a similar motor to your own specifications.
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.