Compare ögonblick to Augenblick for you German learners out there!
Or okamgnienie in polish :) Seems like everyone is blinking; all over the world! :)
I never use it that was personally, but according to Wiktionary, yes.
Not necessarily, it highly depends on context. A moment can be anything from under a second to a few minutes (in my understanding) . If you say "I come in a moment" you won't be there in under a second.
My answer: "I am coming in one moment" was improperly marked wrong. I'd suggest it be added to the possible translations.
Hmm, I had a word-picking exercise for this one and it only offered "while" for ögonblick. Duo seems usually to want to associate stund with while and ögonblick with moment. So I wonder if that's a good exercise.
As far as I know, på and om are not generally interchangeable as expressions of time. på + time span means something requiring that length of time; om + time span means something will happen in the future within that time. I find translations for both "om ett ögonblick" (in a moment) and "på ett ögonblick" (instantly). It seems på emphasizes the brief period of time involved, while om is a more vague expression that could be on the order of minutes, which I think is what's wanted in this sentence (in English, "in a moment" is often stalling for time without giving a specific estimate).
Also, på has many other uses in time expressions (time of day, days of the week, seasons), but I've only encountered this one for om.
That's my analysis, but perhaps a native Swedish speaker can weigh in with a better explanation :)
Native Swedish speaker here, I'm not a linguistics expert but I believe you pretty much got it right.
On the mobile app it translated ögonblick as a while. It's it used that way?
Sort of. It pretty much means "I'll be there soon", though I think a while implicates a longer period of time than for example "a moment" or "a second".
One of the possible uses for "om" (prepositions often have many uses which don't translate neatly from one language to the other) is "within (a period of time)".
Would this mean "I'll be there in a moment"? No comments are appearing so I can't see if that's already been asked :D