Okay, I'll address part of part ("Does it have value to the modern... math-learning audience?") of question 6, and part of question 5, for now.
I've read chapter 1 only (and the main text only, not the marginal notes) so far, and it has definitions, postulates, and theorems from elementary plane geometry, lumping postulates and theorems together (i.e., not caring which are which; indeed, not dealing at all with the fact that some things are definitions and some are postulates and some are theorems). For example, the wider angle of a triangle is opposite the longer side; a quadrilateral with parallel opposite sides has equal opposite sides; etc. (The only misstatement AFAICT in that chapter, in #25, is that if an angle and two sides of one triangle equal an angle and two sides of another triangle, then the remaining angles and side of the triangles are also equal.) This is a reasonable basic-high-school-geometry text, I suppose, but not the way high school geometry is taught nowadays (where a lot of attention is paid to the difference between postulates and theorems, and to proofs). It may also be of some interest to students of the history of mathematics (I don't know), but not to mathematicians.
I'll bl"n get to the remaining chapters (and perhaps the introductions) at a later date.
A later date:
I've now read chapter 2. Most of it deals with proportions. He discusses how if you add the first to the second term in a proportion, and add the third to the fourth, the result is still a valid proportion, and other such manipulations: rather more manipulations than I would have expected (he adds the first to the second, subtracts it, adds the second to the first, subtracts it, etc., etc.), but nothing that's not covered — though some of them as exercises — in a prealgebra class (or so). The last two paragraphs are on another topic: they state, first, that if you do the same thing to both sides of an equation then the result is still a valid equation, and, second, that if a=b and b=c then a=c. Again, this is covered in prealgebra (or so). Nothing of interest to mathematicians here.
An even later date:
I've now read chapter 3. It deals with several topics, all of which seem to be therein order to build up to its two main results, the formula for the area of a circle and the Pythagorean theorem. Along the way he mentions and proves various results from high-school geometry, including that a triangle with two (or three) equal sides (or angles) has two (or three) equal angles (or sides), that corresponding angles formed by two parallel lines with a common transversal are equal, that the area of a triangle is half the base times the altitude, and the like. His two proofs of the Pythagorean theorem are standard, including Euclid's. He proves also that the circumference of a circle is more than three times its diameter, using a proof I haven't seen before, personally, but strongly suspect is well known. Finally, he proves that the area of a circle is half its circumference times its radius, using a method of proof that is by far not rigorous enough for a modern mathematician, but which approximates a standard proof from calculus: take concentric infinitesimal shells and sum their infinitesimal area. Again, there is nothing here that won't be found in many other places (except perhaps his proof that the circumference of a circle is more than three times its diameter, but, again, I doubt it).
Also, re question 5: In the first three chapters, there's no Torah content.
