Makes German easier to understand. A house-animal would be the animal you keep in or at your house. The strength of compound nouns is that they can make more sense, than inventing completely new words you have to learn.
It also makes gender and inflection easier, since only the final noun, Tier in this case, take care of all. Das Tier, Das Haustier, Die Tiere, Die Haustiere. You don't have to care what gender or inflections Haus has. (It's das Haus, die Häuser if you were curious)
no, it does not. Trinken (er trinkt, es trinkt) is used for both humans (human animals) and animals. Essen (er isst, sie isst) is used for Humans, fressen ( es frisst, der Hund frisst, die Katzen fressen) for animals. Essen does not change to fressen. They are separate verbs. Sort of like: to be and to exsist.