Final answer:
The animal that has water-proof eggs, gives live birth, and feeds its young with milk is the platypus, a monotreme that lays leathery eggs and secretes milk from its skin since it lacks nipples.
Step-by-step explanation:
The creature that has water-proof eggs, gives live birth, and nourishes its young with milk from glands is the platypus, which is classified as a monotreme. Monotremes are unique among mammals because they lay eggs with a leathery shell, unlike the hard-shelled eggs of birds, and the eggs are retained inside the mother's body before they are laid in nests. After hatching, the young are nourished by milk secreted by mammary glands directly onto the skin, as they lack nipples. In summary, only the monotreme group, which includes the platypus and echidnas, lays eggs and provides milk to their young without the presence of nipples.
Monotremes are a distinct group within mammals with only a few living species, such as the platypus and echidnas. The platypus is found in Australia, and together with echidnas from New Guinea, they represent the sole living monotremes. Notable features of monotremes include their lower body temperature compared to other mammals and, in the case of the platypus and echidnas, the absence of teeth in adults.