"Good" is literally "jó", that's why that is a better translation.

But Szép napot! can also be used as a greeting, although it is less common than Jó napot!.

(By the way, I either say Szia! or Jó napot! but never both of them together.)

"Jó napot (kívánok)" is a common greeting when meeting somebody. "Szép napot" is unusual, but not incorrect. I would probably rather use it for saying goodbye. As in "have a nice day". You can also combine the two and say "Szép jó napot!" (for meeting) :)

It should be accepted, I believe.

"(További) szép napot" can be used to say goodbye (it's pretty much like "have a nice day"), and nowadays it's more and more popular as a greeting as well.

It's perfectly correct. In fact, it is "szia, jó napot" which sounds very unnatural. It's two greetings together, which is never used. 'Szia' is a greeting, and "szép napot!" is like 'Have a nice day!". 'Szia, szép napot!' is a common farewell greeting, *'Szia, jó napot!' never occurs.

• jó = good
• jól = well

One is an adjective, one is an adverb.