1) yeah, you can guess the kernel, apply the filter, reguess, reapply, reguess... that's called blind deconvolution and "should" converge at least in some cases.
2) the entropy is the same for blurred and reconstructed image. If I compare source with blurred image, the entropy decreases (naturally). For 16 bit image data it only decreases marginally, though, that's why you can reconstruct the image. I'll try and find numbers for it.
3) rapidly. If I change one (!) pixel in the most blurred image by, say, 10%, the reconstructed image has enormous ringing artifacts. That said, for small blur radii such as in the last image, it's not really noticeable.

thank you

@Joey: Have you taken a look at "sparse codes" before? If no, I'd recommend you do. I saw a master-thesis where blurred images were reconstructed using sparse codes. The results were pretty astonishing.

Yeah, I've thought about something like that already. The problem with the dictionary is, though, that it's only a stochastic process. There is no way of really knowing what the original looked like.

Another idea I might try. Imagine filming something with your low-res (320x240) webcam, let's say you take a movie of a textbook page with 100 frames in total. In principle (this is, excluding noise) you now have recorded the same information as if you had taken a 3200x2400 high-resolution photo of the page. All the text should be readable (given, of course, that you moved the camera). This is already being done in crime investigation and I saw a program which raised the resolution of motion pictures by taking subsequent frames and calculating new frames from them. It all depends on how well your motion detection works, though.

Didn't check the code but how do you determine the fitness of your kernel? Edge counting?

I don't check the fitness. I just think that the output (sometimes) looks better ^^.