I don't understand when to use kdyz or kdezto or zatimco. They all seem to mean "while".
Have you tried Google? :)
když - Wiktionary
kdežto - Wiktionary
zatímco - Wiktionary
Why not, "Já Kateřinu miluju, zatimco on ji nenávidí"?
It should be accepted as a typo, correct is "zatímco".
One more thing... Is there a reason there are no "tips and notes" for this chapter?
Thy haven't been written yet and they are not a current priority.
I left out "Já" since that is implied anyway by miluju. Why is that wrong?
Here you are making a contrast between I and He so it would be strange to leave it implicit.
what is the difference between nesnáší and nenávidí
nenávidět may be stronger but both mean strong dislike including potentially some ideological reasons, xenophobia or similar.