A: While a mathematical theory or proof or equation would not be patentable, a method of doing something useful might be patentable.
As a matter of pride and prestige, it may be worth it to you to pursue a patent on the method, so you can be a patent holder.
On the other hand, as a business and practical matter, assuming you could patent your method of drawing exact angles, how would you enforce your patent rights? You would have to try to get individuals, groups, schools or companies to pay you a license fee in order to use your method. Suing schoolchildren or individual hobbyists and artists is not feasible or popular (and is not likely to make you money or friends.)
A: What you are describing is clearly copyright infringement, and your proposed fair use defense would not fly. The author has a pretty far-reaching right to control and profit from clearly derivative works like a recording of their writings. The law governing this is the same throughout the US. You should ask for written permission from the author (or copyright holder) before doing this.