There are 7 (+1 because of chimeras) classes of animals: Mammals, arthropods (insects, arachnids, myriapods, and crustaceans), molluscs (like slugs, squids and so on), avians (birds), reptiles, amphibians and fish - and chimeras that only live in Faizeon. Chimeras are basically just a combination of different classes of animals, like a mammal-avian or fish-reptile. They are natural creatures and were not artificially created. By the way, animals can still look monstrous even if they are not categorized as such. Something like a red four-legged creature that looks like a beast but is still a mammal is an animal. Monsters have specific types.
Plants of all kinds are grouped together into flora since there are too many different types to give each its own category. The specific type can be noted in their entries. (Disclaimer: I'm no biologist and I know there are probably more than 7 classes, this is to keep it simple.)
Bauleura only. Most Gigant species are usually mammals but there are a few exceptions here and there. They do not really live in certain habitats - except the bigger ones that have their own dominions - and often wander around. Some of them can become a threat to cities but they are not vicious in nature. Gigants are still animals and not counted as monsters.