How is instinct carried from one generation to another? How can non-structural information, specifically instinct (a fixed pattern of behavior that an organism reverts to as a response to certain stimuli), be passed on from generation to generation (such as an unborn baby's instinct to begin inhaling and exhaling amniotic fluid while still in the mother's womb to "practice" breathing, a sea turtle's inclination to enter the sea after hatching, etc.)? Does DNA have anything to do with it? I can't imagine what else it could be, considering that the genome is the only thing an organism passes on to it's progeny.

This stuff is hard-wired into either the organism's nervous system, or endocrine signalling pathways (e.g., hormones), or possibly a combination of those two mechanisms. In that sense, yes it is encoded in the genome, but not in a language that we can understand or interpret yet. Also, don't overlook all of the macromolecules that the female provides to the developing egg during oogenesis, your mother gave you lots of things besides a copy of her genome--you just don't have any of those macromolecules left now--but you wouldn't be here without them.