By being a nice person, just like how one would hold open a door for someone else? Though, that aside, when you say "Guten Morgen", you aren't wishing anything. It's just being polite while at the same time, you are saying something about yourself. For example, you could simply say "Morgen" which would mean you are in a hurry, or, depending on how you said it, that the morning isn't good at all. There are a lot of applications for "Guten Morgen". It all depends on how you say it and in which situation you do it. Anyway, it's not comparable to the questions in your posts as "Guten Morgen" can never be fake. Something like "Wie geht's?" (how are you?) would be more fitting, although it's rarely used as a greeting and more often than not, it would be meant seriously.
This is the same BTW in Hungarian. Even better, in HU we still have the form of "I wish (you) a good{Acc} morning", however a bit less formal way you can say just "a good{Acc} morning"
This simplification happened to German earlier too. In fact, my German old lady neighbor still to this day says every time: "Ich wünsche Ihnen einen guten Morgen / schönen Tag, Herr kmarc"
"How are you?"
"I'm well, and you?"
"Great, thanks."
It's just a ritualistic exchange.
How do you do?
To which the correct response is:
How do you do?
I was told by a Chinese colleague that this is a very informal greeting, strictly between friends - pals, rather.
I didn't ask, at the time, because I was more preoccupied with trying to pronounce it (my colleague was very helpful). But I would like to know the context behind this. I mean, what is it in asking about having eaten that signifies a greeting?
In Greek, for instance, we say "yia sou" ("γειά σου"), for "hello". It means, basically, "have health". To me (well of course it would) it makes sense to wish something good as a greeting, I think "shalom" for example, means "peace", etc. I don't get the "have you eaten" greeting and I'm very very curious. All help in this matter is deeply appreciated :)
If you eat well, you'll grow healthy, if you eat poorly, you'll grow unhealthy. They stem from the same principles :-)
OTOH I wouldn't call these "fake"; It's common, it's certainly different than how I socialized, possibly it's greatly misunderstood by many. Along the same train of thought, other languages' greetings would also be fake... After all, how could I genuinely wish a random German stranger a "Guten Morgen" or what do I care if "你吃了吗?" (lit. "have you already eaten?")
Let's rather be grateful for these questions not having to be genuine. Chances are high that when you ask someone today how they are (in their health) or if they ate (because there's no food shortage), then they can simply reply with a positive answer.