You might find the distinction between information and data easier if you think about a word processor file. You may write the same English text into a "word" document or into a wordperfect document. The data in the two files would be quite different but would be interpreted by English speaking readers in the same way. However, a non-English speaking readers might place a different interpretation. Information comes from data and from interpretation.
There is, in fact, very little information in DNA. The external shape and chemistry of the double helix is very uniform, regardless of its base sequence.
This is nonsensical. The shape and chemistry of the transistors comprising the memory image containing a "Word" document are also very uniform, but that doesn't prevent the document, or the computer's memory, from containing information. It merely means that you're looking in the wrong place for it and using the wrong tools. DNA contains a tremendous amount of information stored in the base pairs. In order to extract that information, the double helix is "unzipped" (which makes the base "pairs" much more chemically active, since they're now exposed to the rest of the world).
I may not be able to read a Word document by eyeball, but that doesn't mean that the document contains no information. It merely means that if I'm stupid enough to go looking for something with the wrong tool, I won't find it. I don't use microscopes as metal detectors, either.