It seems like your idea of "matter" might best be understood as "anything that can be measured." And given the equivalence of matter and energy (E = mc^2) I think "matter/energy" or even just "energy" would do fine.
As for the "laws of nature" that govern matter/energy - I don't know if they "exist" independently of matter/energy or if they should be thought of as "existing" only when there is some "stuff" around.
As for information - I don't understand why you would want to define it in terms of DNA/RNA. Yes, DNA stores information, but the concept of information extends well beyond DNA. For example, this post contains information but no DNA.
So with these clarifications, I will attempt to answer your questions:
A) Anti-matter is just a type of matter. Whether matter/energy has always existed is unknown, but we our current theory says that both matter and time "began" with the Big Bang about 13.7 billion years ago. But it is possible that the matter/energy has always existed and the universe cycles through Big Bangs and Big Crunches, or that the matter/energy of this universe came from a larger "parent" universe. These questions cannot be answered with any certainty given our current scientific understanding.
B) I think it makes the most sense to say that natural laws exists independently of matter/energy. But that leads directly to the philosophical quagmire of ontology (What does it mean to "exist?" What does "is" mean?).
C) Darkness is defined as the absence of light.
D) The origin of DNA is one of the biggest scientific mysteries. The question if information always "existed" leads us back to the quagmire of ontology. What does it mean to say that "information" exists if it is not physically manifested in a medium like a CD or book or movie or mind? But if Mind is the foundation of Reality, then yes, I would say that information has always existed.
E) Yes, that is possible. It's called "Panpsychism." It's also possible that Matter and Mind are aspects of the "One Reality" or "Universal Mind" or "Mind of God." It could be "Matter/Mind."