Wouldn't это животное mean "this animal"? I thought the whole sentence meant "this animal is a wolf".
/edit: I think I got it. This is literally "a/the wolf – this is an animal" -> "a/the wolf is an animal", right?
The emphatic это is often used in sentences that are definitions. It is not translated there (for the obvious reason that it does correspond to anything in English).
It used to mean exactly that. However in modern Russian the word "живот" no longer means "life" (it means "abdomen" instead), and the connection between "living" and "животное" is mostly lost.
So, when copula is missing (almost always) is followed the order subject - direct object (actually in italian it would be literally "nominal predicate", not aware of the english designation)? Is this strictly followed order?
Pretty much. You may (try to) fight this word order by using intonation, with the most likely outcome being confusing the listener.
In the past and future tenses it is a bit easier since you will most likely use Instrumental there for the subject complement of the predicate nominal or adjective (the thing introduced into the sentence with a copula). Still, starting with a subject is by far the most common way (even when you do have choice).
The copula is usually zero in the present tense. The verb быть is easily found in the past and future.
Note that making a noun or an adjective into a valid predicate is not the only meaning of the verb "to be". When existence is emphatically asserted or rejected, we use есть/нет. When the place of an object is identified, we may use «находиться» ("to be located") or another placement verb. English rarely specifies that objects "stand", "lie" or "hang" somewhere. Russian uses these verbs often.
"Животное" is any animal including birds, insects, amphibians, etc. "Зверь" is technically a mammal, though it's not a scientific term for them (that would be "млекопитающее"), it's also close in meaning to "a beast".
It is masculine. As are consonat-ending кит, кот, пёс, слон, верблюд, бобр, енот, лев, ворон, дрозд, воробей, скворец, дельфин, жираф, бегемот, крокодил and also голубь, медведь, олень, лось, окунь.