My first question: Using of articles at animals
I am not good at Greek language but I'm trying to. I have trouble at answering for the appropriate article for every animal it follows. For example, the letter 'η' is used as feminine like 'η γυναικα'. Why it is also used for cats ('η γατα')? The same with butterfly, 'μια πεταλουδα', even though that 'μια' is used as feminine, why they are using it at animals. Another one is the ape, 'ο πιθηκος', even though 'ο' is used as masculine.
Why not 'ενα', it is used as neuter if the gender is not identified. I want to know how and why. I want answer, not insult.
in greek animals are either ο , η or το , the grammar rules you just mentioned exist in other languages not greek, every language has its own grammar rules. When speaking generally you have to say η γατα but if you know that the gender is masculine you can say ο γατος. To describe it simply every animal has a specific gender article when you dont know its gender, but when you know it you can use it in some cases while in some other you dont, for example even if you know that the monkey is feminine you never use η, or if you know that the deer is masculine you never say ο , you can only say το ελαφι or η ελαφινα if its feminine.
When I typed 'ενα πεταλουδα', I'm wrong. It should be 'μια πεταλουδα'. But how can I know that the butterfly is girl since it used 'μια'.
also(most of the times except few exceptions)feminine animals end with η or α and masculine with ος
The gender matches the word, not the sex of the animal. In the same way that a chair or spoon have no biological gender, but the words for those things have a gender. Πεταλούδα as a word is feminine, regardless of the sex of the actual insect. As for knowing what the correct gender and hence answer is, it's all about the endings and memorising them.
An exception is the word for cat, as both γάτος (m) and γάτα (f) exist. It's fine to use either when you don't know the gender of the cat, and once you find out you can use the appropriate one.