Thank you so much, Paulina! You're amazing! You've helped me so much!
No problem, I'm happy to help (whenever I'm able to) :)
The first is about this Kasia/Kasiu thing -- would a parent be more likely to use Kasiu, as well, if they were saying good night to their daughter, or whatever?
Yes, probably, I think so. But I guess a parent would be more likely to either say only "Dobranoc" (Good night) or "Dobranoc, córciu/córcia" (diminutive for "daughter") or use some term of endearment (usually if the kid is young) like "kochanie" (darling, sweety), "skarbeczku" (the vocative case of diminutive form of "treasure"), "słoneczko" (diminutive for sun), etc. etc. etc.
I would say it also depends on the parents and their relationship with their children - if parents are more "cool" and "easygoing" they can say "Dobranoc, Kasia" or "Dobranoc, Kaśka" and it will sound OK.
Btw, diminutive forms of "Katarzyna" don't end with "Kasia" - the sweetest is probably "Kasieńka" and more funny but still sweet is "Kasiulka", "Kasiulek", "Kasiuleczek" lol
The second is (and this is really just out of curiosity), I've read that before the Second World War, the vocative case tended to be used more often, but post-war, the nominative case has become increasingly widespread...do you know if this is true?
I honestly don't know, but I guess it could be. It is usually believed that the pre-war people in Poland were more cultured, well-mannered.
In more formal situations we still use the vocative case: "Panie doktorze" (Mr. doctor), "Panie profesorze" (Mr. professor), "Panie dyrektorze" (Mr. director) or at work, for example: "Pani Kasiu" (no matter if Kasia is a director of a company or a cleaning lady) or when you're addressing your neighbours, for example.