Yes, the edges are impressive, aren't they? The ice is floating, almost flat, and has had hundreds of years to reach equilibrium, so there's practically zero vertical shear stress in the ice shelf. As well as that, the ice itself is very laterally homogeneous - there are layers within it, but all the horizontal variability is on scales of kilometers or more. There are no particular faults or planes of weakness within the material. This means that when it breaks under tension, like this, it breaks in a very clean and even way.
Also, remember, you're only seeing the top 10% or so of the berg. There can be interesting shapes below the waterline, caused by preferential melting.
As for the glaciers feeding the shelf, that's an interesting question. Floating ice on its own provides very little resistance to their flow, but the mouth of the ice shelf is narrower than the back, so the converging flow has a resistive effect, like squeezing toothpaste out of a tube. If a gap is made in the ice blocking the mouth, then there should be some speedup of the glaciers. It all depends on exactly where the rift goes next, and on the exact balance of stresses in the shelf, which there's some uncertainty about.