Any 4 bit sequence can be squeezed into 1 bit if you have a restoring algorithm that works - it's a trivial case.
In general, graphics are notoriously incompressible without allowing for loss of data (i.e., the JPEG format).
Sure, for some tightly written assembly language code (i.e., optimized) attempts at compression are probably pointless. Is that how you would describe the DNA "code"?
With respect to your remarks about cell functions, I do not think that your conclusions are justified by your arguments.
I don't believe you're serious but I try again. I have a 15 gallon gas tank and I want to know how much gas is in it with 1 gallon resolution and all you get is 1 bit to tell me. It works great if it's full or empty but how do you tell me I have 5 gallons? What kind of decompression algorithm is going to take 1 bit and tell me that? I'm biting my tongue here.