Nice try, Duo dog

I laughed so much, thanks man.

(Lolcat speech) I arz catz, c? I iz NOT weareeng costyoom. I can haz cheezberger plz?

(English) I'm a cat, see? I am NOT wearing a costume. Can I have a cheeseburger please?

Yes. A sentence like this is also correct: "Jestem nie psem, ale kotem", but then the noun is negated and the meaning is slightly different ("It's not a dog who I am, but a cat").

"Deep down inside, we're all cat, right?"

"Kot" and "pies" are in Nominative case and "kotem" and "psem" are in Instrumental. "Psa" is Genitive. Although it might seem bit strange for a non-native speaker, we use Instrumental case with verb być (to be) talking for example about your/someone else's job/nationality/identity. There is some explanation about Instrumental case here: https://www.duolingo.com/skill/pl/Defining.

It should be there, the audio exercises are on, must be some bug.