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OK a few things that can be kind of confusing in those books seem to have messed with you.
1) Dark matter isn't particularly magical stuff. Its actually a pretty broad categories which includes anything thats not actively glowing (like say the earth, black holes and suns that have gone out) I have never heard any reference of dark matter being higher dimensional.
2) The theory as it goes (last I checked, it keeps on changing) is that our 4 dimensions (the three traditional ones and time) are large and open, and that there are either 6 or 7 more dimensions which are "curled up" very tight. To be perfectly honest I don't know what that means, but I have seen the phrase several times, and its how Hawking's explained it when he lectured at my university. (on an unrelated note Hawking's makes for a really creepy lecturer, my room mate worked sound for him, they didn't have to mike him, they just plugged the sound system into a little box on his wheelchair)
As to your complaints about relations between 4D and 3D being treated the same way as relations between 3d and 2d, well, its honestly all we have to work with. Humans have a lot of trouble grasping something that is 4d, but we can handle 2d quite well. Essentially what is done is we take what we understand 2d/3d and try to extrapolate general rules from that. The hypercube cross (did you catch that picture by Dali in the hyperspace book? its the one with Christ on the hypercube) makes sense if you think about it. just remember that its solid, and will make a hollow hypercube.
On a side note, if you liked A brief history of time and Hyperspace you might want to look into a book called "Godel, Echer, Bach... Eternal golden braid"
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Use the star one and you'll be fighting off the old ones with your bare hands
-A Shoggoth on the Roof
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