In mainland China, it is common to say 早上好. In Taiwan, it is 早安. Don't know why the course contributors do not make 早上好 the standard translation for simplified Chinese.
Peace (平安), safety (安全) clean (安静)…in these phrases I think of it as sort of wishing peace and safety.
Dialects in China are pretty much independent languages so idk maybe some use tăo but that's irrelevant because standard Mandarin only use zăo.
If you listen closely (and think about the Z) it is actually zao, a very weird one though. If it was tao the T would undergo aspiration and would sound different.
Actually, if you're just saying "morning!", you'd say "早!", even though "早上" is translated as "morning". Not every word/phrase can be translated exactly, especially, if it's a greeting or goodbye.
The second character 安 (ān) means "peace." So, the literal translation of 早安 (zǎo ān) is "morning peace".
I always thought it was 早上好, that is what was spoken in Shanghai, I think that it what people mostly say. I prefer to say 早上好 because it is more natural, but is there a difference?