Embarrassing moments in the recent history of evolution

Dr. Jack Horner, one the the world's leading paleontologists, refuses to allow a T. rex specimen to be submitted for carbon-14 dating, because he knows it might erode the theory of evolution.
Dr. Richard Dawkins, the world's most well-known evolutionary biologist, cannot answer a fundamental question:  Has a mutation ever been documented to result in increased genetic information?

How does the theory of evolution explain these phenomena?

The mantis shrimp of indo-pacific reefs has an irreducibly complex weapon that utilizes energy storage in a unique mechanism, impossible to explain through evolution.

The male Japanese puffer fish spends over a week creating an artistic sand sculpture to attract a female.  This defies evolutionary explanations.

The Lyrebird of south Australia has an ability to imitate sounds that defies belief.  

Consider the digital code that would be required to enable this unintelligent spider to spin this intricate web.