What is czy? It translates as is but so does to so what is happening here
'Czy' is a special word for questions, which expect the Y/N answer. Can be ommited in spoken language (because of the intonation): 'Pająk to zwierzę?'
It is also a conjunction in some cases (or, or rather).
'czy' is a word which you can put in the beginning of a question sentence to indicate that it is a yes/no question.
Well, as both "a spider" and "an animal" are noun phrases, there are two options here: "Czy pająk to zwierzę" (Nominative) and "Czy pająk jest zwierzęciem" (Instrumental).
I entered it as "A spider is not an animal?", and I was marked wrong. In spoken English, the intonation would indicate that being a question, despite the word order. Is it different for Polish?
We allow it, if the Polish question did not use "czy". Then we can claim that it can be also a surprised "What? A spider is not an animal?".
But as here we had "czy", you have to translate it with a question word order. "czy" makes it clear that this is a real question.
I think "A spider is not an animal" would be "To pajak to nie zwierzę?" Obviously different from "Is a spider an animal?" which is "Czy pajak to zierzę?" OR just with intonation Pajak to zwierzę?
"To pająk" only makes sense if you want to say "this is a spider". If you want to say "this spider", it's "ten pająk".
Both "Czy pająk to zwierzę?" and "Pająk to zwierzę?" can work for "Is a spider an animal?", the first one is better because "czy" makes it clear it's a question.