It is quite possible that if I were to read lots of papers by Behe, Dembski, or other ID proponents, I would find many of the contradictions that you assert. Maybe these guys are complete morons who can't utter more than a few sentences without contradicting themselves. I don't know.
However, I have read one and only one paper all the way through, and in it, they gave a definition of irreducible complexity. That definition was posted previously. I have read a bunch of other snippets, media reports, blog postings and such, and they all agree.
Irreducible complexity is a simple definition. It doesn't say anything at all about evoloution. It doesn't say anything at all about intelligent design. It doesn't say anything at all about biology. (The first example of an IC system I ever read was a mousetrap.) "Irreducibly complex" is an adjectival phrase that describes a multi-part system that won't function if you take out one of the parts. That's it. Period. End of sentence. No ID. No theistic evolution. No evolution. No biology. Done.
My body is an irreducibly complex system because my liver, or lungs, or stomach, or whatever, is necessary for its continued function. That isn't a statement about evolution or intelligent design. My computer is irreducibly complex because it needs a CPU to operate. That's a definition. And I would be very surprised if you could find a contradiction to that statement in the writings of ID proponents.
Well, your body is not irreducibly complex. There are many many things you could do without. In fact, you can do without a good portion of your liver. So then, IC must redefine a human to be a certain number of parts (like a mousetrap) that it cannot do without. As such, it is such a loose and sloppy definition, subject to revision by medical science, that it fails completely.
But the point is that IC is used as a hammer to disprove evolution. You cannot deny (if you have read much of their works) that this is the purpose that Behe and others have crafted that definition for.
"Evolution cannot be true because what good is half an eye." That is a strawman that suggests evolution proposes "half-eyes".
They suggest a mousetrap must have all of it's parts. But a moustrap with a weaker spring is still a mousetrap. A mousetrap with a stickier trigger is still a mousetrap. If mousetraps evolved, they would go through stages where the parts improved (by natural selection). There would not be a mousetrap without a spring.
If you don't think ID proponants are using irreducible complexity to deny the mechanics of evolution, why do you suppose they are bringing up the concept?
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Edited to add parable:
I'm reminded of the old story that illustrates bad conclusions:
A scientist had a dog that loved to fetch sticks. He would throw the stick and say "fetch" and the dog would run after the stick and retrieve it. But he decided one day to experiment on the dog (being the cruel man that all scientists are). He surgically removed one of the dog's legs. After the scar had healed, he took a stick and threw it and said "fetch". Though limping, the dog gamely went out and brought back the stick. So the scientist removed another leg and repeated the experiment after the scars had healed. Severely hobbled though he was, the dog managed to hop around on two legs until he could retrieve the stick. Once again, the dog went under the knife and when he had healed, the scientist threw the stick and said "fetch". Even with only a single leg the dog so loved the game that he dragged himself out into the yard, got the stick in his mouth and dragged himself back. So the scientist removed the final leg. He took the limbless dog into the yard, threw the stick and yelled "fetch", but the poor dog just looked at him helplessly. The scientist concluded, "When you remove all of a dog's legs, it becomes deaf."
This is the sort of conclusion that ID-ers are making about evolution. If you remove a part and the organism no longer works, then that part was what was making the organism work.
