Violation of copyright "if you try to pass the 'derivative' work off as the work of the other guy"? You are mixing up art forgery and copyright violations. Quite different.
In fact, if you use a photograph as a direct guide for a derivative painting without getting permission from the photograph's copyright holder, the you will be violating copyright. It's simply a matter of whether the copyright holder decides to press the issue. Even Andy Warhol was sued for using Patricia Caulfield's photograph in his prints. And since trademarks are not about image ownership, but rather brand association, it's perfectly fine to use a trademarked image in transformative way and in a different market or industry than the commercial sector that the trademark actually exists in. In Warhol's case, it helped that Campbell's Soup enjoyed his works, but it wasn't the deciding factor.
I understand you're not claiming your description is how IP works, and just how you wished it worked, but you're way off base from the current legal system. You're right that there's a scale, and it's often the whole point of a lawsuit to decide where on the scale your work actually falls. There are guidelines, but it still has to be decided on a case-by-case basis. The reason you can do an interpretation on the Mona Lisa is because it is not protected by copyright (Public Domain!). A cubist interpretation of a current work still under copyright protection, if identifiable as a derivative work (or if you say you derived it from another work), would fall under the regulations of copyright derivatives. Then it's up to the court and jury to decide if you were co-opting too much of the protected work (and it wouldn't help that you were working in the same format -- 2D visual art). Using the same subject matter as depicted in an existing work is not a violation of copyright unless you were using their actual work as the source (at least as far as the other side can successfully demonstrate that to a jury). IANAL, etc.
I would also re-include differentiation to that list.
Not in the explicit sense of formal differentiation, but in the general sense of the slope of the line tangent to a curve, or the rate of change of some value. People should have the basics of velocity and acceleration before starting physics 101, especially since it's easy to go through the entire education system without taking any physics classes. That sort of understanding lays the groundwork for thinking about interrelated systems, and dependent behaviors that are neither directly nor indirectly related to a parent process, but rather derived from it.
Well, local used-books shops might be accurately pricing their books for the local market, which could differ from the nationwide market on the internet. If the local stores were forced to price to the national market, they might not be able to sell those books to their usual customers, and not even the used-book arbitrage traders would want to buy them. This could, in the long run, significantly reduce the thrift bookstore revenues and drive some out of business.
And like GP pointed out, some of the hidden treasures in the book stores act as sales to draw in customers to the store, who might buy other books as well. If the arbitrage trades come in and snatch up the "sale" items, the stores are forced to eat the discount instead of generating more revenue.
Scientists will study your brain to learn more about your distant cousin, Man.