The creators clearly had something more idiomatic in mind, but obviously that's correct as well. Added.
So, why is "Dzien i nov" = Day and night ...if "Rano i Wieczorem" is "in the morning and in the evening"?
To clarify it more straightforwardly, it's a matter of case:
"Dzień i noc" (nominative case) = "[the] day and [the] night"
"Rano i wieczór" (nominative case) = "[the] morning and [the] evening"
"Dniem i nocą" (instrumental case) = "in [the] day and in [the] night"
"Rano i wieczorem" (instrumental case) = "in [the] morning and in [the] evening"
Notice that "rano" is the same in both cases.
"In the day and in the night" would be either "Dniem i nocą" (similarly to "rano i wieczorem"), or more literally "w dzień i w nocy" (the form "w dniu" is rather used when you mean a specific day, like "w dniu jutrzejszym" = "in tomorrow day", to translate it literally. 'jutrzejszy' is an adjective from 'jutro')
Yes, but it's not literal. We don't have a specific greeting for the morning nor one for afternoon, and English rather doesn't use "Good day".
Well, if the developers didn't decide to accept & for 'and', then it doesn't work.