I highly suggest to wait just a few more skills. It will be the topic of one them. In between you can check wiktionary https://en.wiktionary.org/wiki/dobr%C3%BD#Declension Note that the phrases here mostly use the accusative case.
Not really. "Dobrou noc" and "good night" are both for leave-taking, for when you are leaving someone at night. "Ahoj" goes both ways, hi/bye, and the translation we chose as the main one reflects going just one way instead of leaving half a sec after meeting or saying each greeting to a different person. "Hi" is included in the accepted translations.
Well... this is not Google, Wikipedia, or Russian. Dobrý den does literally mean, "Good day," but it is routinely used as the generic greeting, "Hello." The less formal "Hi" would more likely be Ahoj on the Czech side -- and Ahoj is also routinely used as the less formal "Bye." The things we have to get used to when studying languages... :-)