Once upon a time, there was a prisoner in solitary confinement, a former public enemy number one of France, aside the wards alone in the prison and allowed only to read science books. When he came across an astronomy textbook by Lagrange, he suddenly had the same idea as you express. http://ideafoundlings.blogspot.com/2009/10/nemo-eternal-returning.html
What do you think I would not undestand? Hinton's Cubes share since ages a bad reputation of disturbing the minds of his followers, fitting nicely to contemporary theories of learning and habit-development of the brain. Only two mathematicians seem to have profited from an exposition to them in their childhood. Ans the one who played around with constructing 3D/4D-analogues to Penrose/Escher 2D/3D-"impossible figure" doubted that such an endeavor woud threaten his health. The info on Talmud etc. came from a well known scholar. Both examples fit to the questions above.
Not quite so. The n-Lab contains a page on it: http://ncatlab.org/nlab/show/hyperstructure , but that is not that new. The usual deficiency of such constructs (and the many attempted definitions of n-categories) is their reliance on set theory. Grothendieck seems to have been the first to suggest to forget set theory as foundations, and Voevodsky's way to build a homotopy-theoretic foundation of mathematics on some sort of computer language (leading to entirely new approaches to artificial theorem proving/checking): http://ncatlab.org/nlab/show/hyperstructure may be interesting for Baas' ideas too. Interestingly too, homotopy theory, n-category were caused by attempts to deal with topology, and Baas' concepts come from the same background. He was apparently motivated by Charles Ehresmann's ctitique that n-categories should be insufficient.
That is hard to estimate, but I think I need the same or less time for studying them. But of course the issue is how one reads them and how much one spends into extracting the hidden ideas and translating them into one's own mental structures (instead of turning one's mind into an emulation of the author's one) . One can study and understand very advanced papers fast and well without a productive "translation", and the more one knows, the easier it is to restrict reading that way.