In this sense the ant colony could be viewed as a single organism, as most ants are clones and carry 100% compliment of DNA. Perhaps not unlike the cells that are shed from our skin to protect the rest of the body...
Wrong.
They're haplo-diploid. Their sex determination system is based not on an X-Y chromosome, but the number of pairs of chromosomes. All the females have 2n, while the males have 1n. This means that unfertilized eggs laid become males, while fertilized eggs become females. While this doesn't equal 100% relatedness between individuals in a colony, workers are full sisters, even more so than us mammals- they share 3/4 their genetic material, as opposed to 1/2.
Not necessarily. They are merely genes that do not die ie get reproduced.
Well, given the common set of assumptions that evolutionary geneticists make, these two statements are near equivocal for the vast majority of cases.
The ant "sacrificed" itself. The gene did not. The choice, such as it is, is made by the ant. To the gene there is no difference.
But that choice would have been impossible to arrive at without those genes. Genes seem to have more direct action on behaviors when there are fewer layers of action between environment and behavior. Us humans are practically black boxes when it comes to environmental stimuli and our responses. Prokaryotes, on the other hand, literally have their behavior controlle by the surrounding environment with ROSE riboswitches. These riboswitches function as thermometers, where heat shock proteins are translated when the mRNAs melt enough to allow RNA pol access.