pretty good. FWIW, my degree is in Materials Science and Engineering, but carbon fiber is not my specialty, and I'm shooting from the hip too. But there is one part where I think you're slightly off base.
A fiber has absolutely no strength in compression, tension only. I can easily hang from a rope, but in no way can it support me like the legs of your chair do. Those finger traps are basically what you would have if your rod blank didn't have any resin/epoxy/bonding agent in the mix.
True in the untempered condition, a carbon fiber is like a rope, or a wet noodle. However, when tempered that all changes, and a carbon fiber thread becomes quite stiff, more like a rod, even without any resin at all.
Structurally, a "carbon fiber" itself is a thread made up of millions of tiny graphene tubes, each of them VERY stiff (like, diamond stiff), but of course since there's millions that are relatively weakly connected, and the joints between them are like millions of "hinges", making the macro structure ropelike. When baked, all of these little fibers cross-link with one another, to create a stiffer structure. So the heat does far more than melt the resin, it also alters the structure of the carbon fiber threads themselves.
So, once heat treated, a single carbon fiber does indeed have some strength in compression! But I agree the resin is needed to bond the fibers together. The macro-fibers may be stiff, but they're still unconnected or at least weakly connected to one another. Imagine a stack of drinking straws unbonded to each other. The resin holds them in place.
Modulus, in any material (as in Young's Modulus), is a measure of elasticity, the equation is stress/strain. On a stress-strain curve, it is the slope prior to the yield point of the material. Elasticity, of course, is how much the material will non-permanently deform. Rubber bands and springs are examples of highly elastic (low modulus) materials, they can be deformed quite considerably without permanently altering the structure. All materials do this to some degree. A high modulus material is stiffer, more brittle, and less "stretchy".
As you said, when a rod is cast, the carbon fibers on one side are in tension, and on the other in compression. A high modulus will allow less "stretch" in tension and less compression on the other side, therefore limiting the movement of the rod, making the rod stiffer.
Now, as for the action of a rod, modulus of the carbon fiber would be only one variable a maker could play with to make a fly rod faster or slower. A thousand rubber bands under 10 lbs of force deform less than 1 rubber band would. Thread density and thickness, thickness of the walls, taper, etc. all come into play. But a high modulus graphite would allow the designer to use less material to achieve a desired stiffness, making the rod lighter. But also more brittle.
FWIW, I'm a metals guy. The success of metals has to do with toughness. On a stress strain curve, it's the area under the curve, a measure of the energy the material can absorb before catastrophic failure.
Metals aren't as strong as ceramics, but much tougher. Take a diamond, the strongest material on Earth, and hit it with a hammer. You get diamond powder. Hit a hunk of steel with a hammer, you might leave a dent.
