I have recently come across the phrase 你好啊 and I was curious about its usage. It was in the FSI Chinese course with a meaning of 'How are you?', but I have only heard 你好吗 on other courses and when talking to Chinese speakers on Skype. Is this because 你好啊 is not really used very much in everyday life, or is it because Chinese speakers tend to tailor the way they say things to suit the level of the other person and 你好吗 is more common in text books?
Usually people just say 你好 because, well, it's just the common way. I don't think there are any reasons.
你好啊 sounds like talking to babies, or if you are greeting someone who is some distance away and you want yourself to be heard. 你——好——啊——
你好吗 is a direct translation of "How are you?" It is only used by Chinese when one really wants to know what is going on with the other, or it may be used with English speakers to make them feel less culturally alienated.
In Chinese, 你好 actually has a common usage with Hello in English, it will be used by the time you want to say hi to people. But the difference between them is, I don't think Hello has a specific meaning in English, but 你好 in Chinese do have a specific meaning. To understand this better, you must know this first, in Chinese, every single word in chinese hold a specific meaning.
你好吗, as opposed to 你好, is seldom used because it implies asking whether the other person has or has not overcome some past problem or medical affliction.
So, 你好 is straight forwardly wishing someone well, whereas 你好吗 is akin to an unsolicited question.
If someone says to me 你好吗, I may jokingly reply, 我 有 什 么 不 好？
In English you do not for no specific reason say "How are you today" because it implies you were not that good yesterday or sometime in the recent past.
Finally, a Chinese rarely if ever use 吃了没 to a non-Chinese, though I am not sure of the reverse.