First off, there is nothing in your example that precludes the development of "all organisms on Earth" as coming from a common ancestor from the design boards of an intelligent agent. I think we both understand the sorts design processes and decisions that would go into that sort of project. This isn't to say that life on Earth did begin that way, but the fact that we can define the methods and requirements for doing the job means that it very well could have been a product of design.
Second, there is no need to assume (as your question seems to imply) that intelligent designers had to be active at all steps in the process from "first organism" to human. The two processes could very well work in parallel, with "intelligent interference" being a relatively rare and localized thing. We easily understand this, because it's how we humans practice intelligent design.
Therefore, evolution predicts that any newly found organism should have nucleic acids as its genetic material. If a new organism is observed that uses some other molecule as its genetic material, this would cause evolution to be found to be false.
You need to be very careful when making statements like this one. It's a mistake to equate an information storage medium with the process of evolution. There is no reason to assume that evolution would be disproved because genetic information was encoded in some different form. (Indeed, I think the case for evolution might well be strengthened by it....) For example, "computer-based life" is in some sense possible even today, and it doesn't use nucleic acids to transmit "genetic information." The lack of DNA clearly does not preclude the possibility that "computer-based life" could change through evolutionary processes.
Give me a similar example using ID as a basic principle.
Still not sure what you're asking here, as you have yet to define "ID" in an unambiguous manner, in terms of both its scope and characteristics. Are we talking about ID in the sense of the folks who spliced a jellyfish gene into monkey DNA? That was clearly a case of intelligent design.
Organisms are all related genetically according to the theory of evolution (common descent). Since all organisms are descended from a common ancestor, they must share the same basic genetic material. This is predicted by evolution. ID would certainly not have such a requirement. By ID I am referring to the notion that an intelligent designer actually did intervene in the development of the variety of species seen on earth. From discussing this with you, I get the feeling that we really agree on the issue of evolution, ie that evolution actually is the mechanism for the change observed in organisms. I also agree with you that it is possible that some intelligence did in fact direct this process. Where I believe we disagree is in whether this is a scientific theory or not. I don't think that there is any observation that would cause a reasonable person to say "since I observed this, there's no way that an intelligent being could ever have intervened in the process of the development of life." That's why I asked you to provide me with such an observation. It doesn't have to be something that has actually been observed. (Such as my example of an organism with something other than nucleic acids as its genetic material which has never been observed.) If there's no way to show that an idea is false, it is not science.