An anguillid is a member of the Anguillidae family of creatures, which include freshwater eels.
I'm pretty sure male octopus can't give birth. So i think what you mean is after mating. I found this on google "Octopuses have a semelparous life history strategy, meaning that they spawn once and die. (Iteroparous is the opposite--multiple spawning events over the organism's life time.) Other organisms are semelparous as well--many salmon, Anguillid eels, many types of plants and insects. So why would an animal do this--spawn once and then die? It doesn't make sense right away, but think about it like this: the energy required to reproduce is put into one major effort. Energy is the key here. It is very energetically costly to reproduce--energy put into reproduction is energy that cannot be used for growth and caring for one's self. Reproduction is a "cost" which can mean decreased growth and increased mortality. A semelparous organism spends its life growing (larger size is related to higher fecundity in many organisms) and devoting energy to that before spawning once near the end of its life." The other part of your question--what exactly causes an octupus to die after spawning. Death is apparently controlled by an optic gland secretion released after spawning. The second link below contains a citation (Woodinsky 1977) for a study on the topic.
All animals, fish and humans included, need to take in o2 and eliminate co2. Because in an aquatic environment water is dense and oxygen concentration is low, fish use gills kept moist by the surrounding water to obtain their oxygen needs as in this environment lungs would prove inefficient. When oxygen rich water is passed over their gills, the blood in the capillaries flowing in the opposite direction to the water in a process called counter current exchange, the fish are able to absorb all the oxygen they require. The deoxygenated water then returns to the surrounding water through openings in the side of the pharynx. Most fish are unable to breathe on land because the structure of air does not not support their gills, leading to their collapse. There would also be too much water loss due to evaporation, and both gills and lungs need to remain moist. Lungs remain moist simply because of ther location within the body. Respiration in humans happens when our diaphragm contracts and flattens, muscles in the ribcage moving to allow our lungs to expand with air. To exhale, the muscles relax. While gas exchange happens for fish around their gills, it happens for humans in tiny air sacs in our lungs called alveoli. The blood then carries o2 to all our cells via our many capillaries, tiny blood vessels so numerous that no cell is more than a few millimetres away from one. Once all its oxygen is lost and the co2 wastes have been collected, the deoxygenated blood then travels once more to the lungs to get a fresh supply and to get rid of the co2 which is lost when we exhale, and the process repeats.
Because fish are exothermic (meaning they use heat from outside of their body) they will often become more sluggish or lethargic during winter. Other than that, they will try to keep their same habits. And even pond fish will need a more deeper pond to hibernate.