It means the same, but the sentence you proposed doesn't have the same structure.
No, that's a wrong form. Numerals ending in digits 5-9 (and 0) take Genitive.
Yes... I made a mistake when writing my comment, but it seems that my change of that comment is earlier than your second comment... that's weird.
Anyway, as it's already edited above, 5-9 and 0 endings take Genitive, 1-4 endings take Nominative (BUT NOT -12, -13, -14 endings that also take Genitive).
I learned once that you have to use the word "doba" in polish instead of dzień when speaking about 24 h like in "24 godziny na dobę". Dzień reflects only the daylight-time. Am I wrong?
I would say that dzień is non-specific (context-dependant), same as in English, whereas doba refers to exactly 24 hours. It can't be any different, since daylight is an unsuitable indicator for time. What would you say during polar nights?