2. "Coded information" is defined as a system of symbols used by an encoding and decoding mechanism, which transmits a message that is independent of the communication medium.
I'm not sure that I would agree with this statement with regard to DNA. It seems to require the assumption that the 'message' is independent, I think you would need to make a case for this.
4. Instructions, by definition, require a mapping from probability space A to probability space B. Therefore any set of specific instructions is necessarily a code.
This seems a lot of room for the defintion of instructions to the point that any particular state could be seen as encoding the instructions for the evolution of that state in line with normal physical and chemical interactions, indeed this is the basis of chemically based quantum computing, that the quantum evolution of the molecules involved will produce an answer to the question encoded in their initial state. While a specific state may be imposed on the molecules to allow us to pose a question they are always in the position of encoding the question relevant to their own quantum evolution. Similarly the chemical constituents of DNA are always interacting chemically with their environment in such a way as for the state of the DNA and its environment to encode the evolution of that state including the production of mRNA's etc...
Again you seem to be front loading with the assumption that there was an 'experimenter' as it were who specified information for the initial state of the DNA, but this doesn't need to be the case any more than someone needs to specify any state for it to subsequently evolve in line with physical laws.
Would you not consider the rings in a tree to be encoded with data relating to the seasons during which those rings developed?
TTFN,
WK