Спокойный means calm, добрый means kind. In this group of idioms, night (ночь) is usually used with спокойный in genitive case (it's a contraction of "I wish you good night" - Я желаю тебе спокойной ночи), while other times of the day are used with добрый in nominative case (it's a statement "This is a good morning" - Это "доброе" утро)
Yes, per other replies on other pages:
You have three genders in Russian - masculin (Добрый), feminine (до́брая) and neuter (до́брое). And word " утро" is neuter.
Yes, it is. утро is neuter, день and вечер are both masculine. The feminine version of добрый is добрая.
Mostly, but there are some exceptions where the noun ending could be misleading. http://www.russianlessons.net/grammar/nouns_gender.php http://masterrussian.com/nounsandcases/gender_and_number.htm Perhaps a native Russian would have more information.
Suffixes are also different for different cases as well as for number and gender. http://www.russianlessons.net/grammar/adjectives.php
"Доброе утро, папа." is "Dzień dobry, tato." in Polish. So, I don't get it? Or do you mean the form: did you think it was going to be "добрый"? Day is masculine in Polish and Good day is used for Good morning there. Morning or "утро" is neuter in Russian. Day is masculine in Russian also. https://en.wiktionary.org/wiki/%D1%83%D1%82%D1%80%D0%BE https://en.wiktionary.org/wiki/dzie%C5%84
Did you put "Добрый день"? https://en.wiktionary.org/wiki/%D0%B4%D0%B5%D0%BD%D1%8C
Thank you! I want to learn Polish also, so I will watch out for that! Look at this: https://en.wiktionary.org/wiki/%D0%B7%D0%B0%D0%B2%D1%82%D1%80%D0%B0 Tomorrow in Russian is "завтра" which is from the combination of за and у́тро. So, it is not completely a false friend. It is more that "Good day" is used for "Good morning" in Polish. The Russian morning does not mean the Polish day, but the word for tomorrow is a bit similar.