(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").
When do I use "kotem" instead of "kot"? or "psem" instead of "psa" or pies? Or does another lesson describe that in notes? If not which one?
"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.