"The chicken is not human."
Translation:Το κοτόπουλο δεν είναι ανθρώπινο.
The Greek sentence seems rather strange - it does not express that the chicken is not a human being. Ανθρώπινος, -η, -ο is either used in constructions like η συμπεριφορά του δεν είναι ανθρώπινη - his behavior is not human(e) (i.e. civilized, compassionate etc.), or in combinations like το ανθρώπινο σώμα, η ανθρώπινη μοίρα, η ανθρώπινη δικαιοσύνη etc. [There is another also another sentence in this course Η γάτα είναι ανθρώπινη.]
For the live animal you can use either κοτόπουλο (= young chicken irrespective of gender) which is also used when talking about food, or κότα = hen. So when someone has chickens you can say 'έχει κότες' in general. The rooster is κόκκορας. You can see more about gendered nouns for animals here https://forum.duolingo.com/comment/27198534.
What is the rule for using 'ο' or 'ω'? And 'ι' or 'η'?
It's the same "rule" that you use for choosing between ee and ea in English in words such as "cl..n" or "gr..n" or "m..t".
That is: in modern English, it's simply something you have to memorise, because the different spellings represent what used to be different pronunciations but are now pronounced completely identically.
Just as English schoolchildren have to remember to write "clean" and "green" (not "cleen" or "grean") and that both "meet" and "meat" are words, Greek schoolchildren have to remember to write χορός (dance) but χώρος (space).