Johnny Cake, those arguments (from Michael Behe, yes?) have been disproven many times over. If you read the Dover decision, you'll see where a conservative judge actually called the whole thing "a canard."

Ok, he said "at worst a canard" and I can't remember what the "at best" was.

I mean, you could check youtube if you want an explanation for 1-2. Irreducible complexity has been dead for a while and Behe is officially an embarassment to the university where he works. #3 you can google, assuming that by "mathematical improbabilities" you are referring to the guy who counted all the atoms in the universe, then multiplied over time and determined that the probability of a strand of DNA popping randomly into existence was so unlikely as to be impossible... these people have been debunked everywhere.

#4 though is harder to debunk, mostly because no one has any idea what ID advocates mean when they say "information." Under their view, what possibly couldn't qualify as "information" of some sort? In a way, the shape of a landscape "informs" the air currents moving above it - is that also proof of design? But we've already shown how nature can gradually produce an eye. Why couldn't nature also produce an information storage system?

Me personally, I'm kind of an atheist depending on the asker's definition of "god." And at this point, I'm going to say that it is just idiotic to try to physically or mathematically prove that god exists and intervenes in the universe. Intelligent design represents a number of deluded but well-intentioned individuals chasing after a phantom.