I didn't understand the function of the "זה" in this sentence. I Put "That mouse is an animal", and got marked wrong. :(
What previous lessons taught on omitting "is", works for adjectives, eg.
The fence is high - הגדר גבוהה
but when describing generalities (a mouse, an animal) Hebrew maintains the "is" as זה/הוא/היא
Not only generalities:
Genesis is the band I like the most = ג'נסיס זה הלהקה שאני הכי אוהב
As far as I can see, זה can serve as copula in every predicative sentence except when the predicate is an adjective.
You were close – it's a good translation for "עכבר זה הוא חיה".
The word "זה" is used like "is". you can either say "עכבר הוא חיה" or "עכבר זה חיה".
So again, זה is here functioning as a copula or is this just a colloquialism is be memorized?
I imagine the use of זה as a copula began as a colloqualism, but now is very common and doesn't sound "low". Still I suspect that you won't easily find it in the media, where language editors have a say.
At least you could understand what he was saying! This puts you way ahead of me... :P
There is a gender difference between הוא and היא. Aside from that however, it depends on the context. In this context the two copulas (זה, הוא) are interchangeable.