Translation:How are you?
It really means something like lively, healthy, etc. Saying that it translates to 'how are you?’ is more conceptual and less literal. More literally it would be something like 'Are you in good health?' The important thing is that people will ask, 'げんきですか' in the same way English speakers ask 'how are you?'
The か at the end of a sentence makes it a question.
Past that, "genki" is general well-being while "daijoubu" is in-the-moment. As a greeting or response to a greeting, you use "genki". If you see someone stub their toe or if you're the one who stubbed your toe, you use "daijoubu".
A big difference I learned from "Human Japanese" between this phrase and "How are you?" in English is that this phrase is literally asking "are you well?". Unlike in English where it is common courtesy to ask this often, even more than once a day, this phrase doesn't work that way. Asking if someone is healthy would be strange to ask several times in a short period.
Yes, but only among very casual company because you leave off any honorifics, including the verb. If you're in a strict workplace, you wouldn't respond this way to your boss but you could to fellow cubicle workers you've worked with for several months.
I suppose if you ARE the manager you could get away with using it if you are trying to reinforce a casual atmosphere. It could be perceived as lazy, but that gets into listener bias.
Considering the exercises allow you to use a keyboard, they definitely should accept kanji for an answer. お元気ですか？ is a correct sentence, and it's auto-suggested when I type "genki" on my keyboard. I know these kanji, I know this word. It's really frustrating to play a guessing game each time: would Duo accept my answer with kanji or no?
from what I read in several threads, the contributors are limited by the number of correct answer they can add to those because of how the platform works. This is a duolingo issue with japanese specifically, maybe they can fix it in the future but for now just know that those are a pain in the ass and is better to try pure hiragana first and if you get it wrong just take a mental note of how many kanji is it asking and which ones.
I see people already discussing the use of "o" here, but the main time I've seen it on duolingo has been before nouns involved in questions- such as (in romaji) onamae ha desuka. Is it purely a polite thing or does it also have to do with the fact that you're asking a question?
The phrase is not a topic (は), neither is it a subject (が).
In phrases like "こんばんは", what you're really saying is "So, about this evening..."
In phrases like this one, "genki" is an adjective that literally means "healthy" but is used in this greeting, which is formulated as a question. It's a bit like the British "All right?"
Genki comprises two words- gen/moto (元)= "source of" and ki (気)="spirit energy." If you ever take on a Japanese martial art, you will hear the sensei talk about harnessing your ki to strike or throw. If you ever take on a Chinese martial art, the shifu will talk about harnessing your qi (same word). O is an honorific. So, O genki desu ka kind of translates as, "Is your source of spirit energy present within you?" Literally it translates as, "Is it your/his/her/their source of spirit energy?" with the rest implied. If you have your source of energy, you are well.