Interestingly, on that SO page you linked, someone says that female DNA is less data (756 MB for females vs. 770 MB for males), whereas I would have thought it would be the other way around, since the Y chromosome is smaller than the X. This is why sex-linked diseases tend to affect men rather than women: women have two X chromosomes, so they have two copies of every gene on the X, so if one doesn't work, they can fall back on the other one (unless the faulty gene is dominant rather than recessive, or they have two faulty copies; but both these situations are rare). Men can't do this because many genes on the X chromosome don't have a corresponding allele on the Y chromosome.
Data is not tied to programming. What about data that is collected through observation and just written down on paper or a spreadsheet? Data != programming. They really have nothing to do with each other, other than the fact that programming uses data. But data does not use programming.
DNA is code, not data (hence the term genetic code, rather than genetic data): it consists of instructions that tell cellular hardware (ribosomes) what to do to produce proteins. It's a bit like a Turing machine: it has programs (genes) made of symbols (nucleotide triplets, aka codons) which a read head (ribosome) reads to produce output (peptide chains, which form proteins). So yes, you can definitely say organisms are "programmed" in a programming language.
Have you ever played Bioshock? The first 2 games rely heavily on the concept of genetic modification. Actually, just Google "genetic modification" to get a plethora of real world examples of what we are already doing.
Yep, that's how gene therapy works. You cut the DNA apart with a type of enzyme called a restriction enzyme, insert the code you want, and then recombine it with a type of enzyme called a DNA ligase. You can also use it to cut sections of code out. Cells do it all the time. You can also change existing DNA or replace it by cutting a gene out and putting a new one in its place.
There is also a kind of virus called an endogenous retrovirus. Normal viruses replicate by entering the host cell and using its machinery to produce new viruses from the viral DNA. There are also retroviruses which have RNA instead of DNA; they have to convert their RNA into DNA and then have the host cell produce new copies. However, endogenous retroviruses convert their RNA into DNA and then insert it into the host cell's DNA. The host cell then produces new viruses just like it would proteins. There are millions of ERV genomes present in your DNA right now, because occasionally they infect sex cells (sperm or ova) and occasionally those sex cells go on to form new organisms as sex cells are supposed to do. Usually the viral genomes get deactivated by mutations, so they can't be produced by the cell. There is one that's still active though, because it's more prevalent in some families than others no there isn't, it was active in the last 5 million years since the divergence of humans and chimpanzees.