must be "My favourite wild animal is a whale."

1 would be correct if you speak of just one whale. But rather say "whales are my favorite"

#3 is the only correct choice. #1 makes sense only if you are talking about one specific whale, for example a pet. However, few people have pet whales. It would be difficult to manage one. #2 confuses singular and plural. However, "Whales." would be an acceptable answer - not as good as "the whale", but acceptable. #4 needs "the". However, if you are talking about your eating habits, #4 is a good answer. I hope nobody eats whale, but if they do, #4 would be the right way to say so.

4 is ungrammatical. The other 3 aren’t but still sound odd. This is because there are many species of whale and the question suggests that it’s asking for a specific species. A:What’s your favorite type of animal? B:Whales. A:What’s your favorite species of wild animal? B:The biggest one. The blue whale.

I'd only reply with "whales". I feel it sounds more natural.