Can you still say Wir kamen von dem Flughafen or do you always have to condense von dem into vom?
No that's wrong. If you mean an airport in general, then you'll use vom. But if you want to use a demonstrative pronoun (i.e one signifying a specific airport) you won't contract von and dem.
Ich komme vom Flughafen. (I'm coming from the airport.) Ich komme von dem Flughafen. (I'm coming from THAT airport).
It does, and you're correct. Strictly speaking, the correct translation of "Wir kamen vom Flughafen" is either "We came from the airport" OR "We were coming from the airport", depending on context. And since there is no context to be guided by, Duolingo should count either version correct.
Yes, " ankommen" was used in an earlier lesson, so not allowing " We came from the airport "seems inconsistent
shouldn't this phrase be in akkusative mode because it gives us a movement perspective? (wir kamen von den Flughafen)
Movement perspective works only with direction, not origin. So "Ich stelle den Teller auf deN Tisch (acc.)" as opposed to "Der Teller ist auf deM Tisch (dat.)", but both "Ich nehme den Teller vom (von dem) Tisch (dat.)" and "Sie sind von der Schweiz". That probably also has something to do with the fact that origin implies movement anyway, so there's no need to differentiate the two cases--unless it is metaphorical, but then accusative or dative constructions are rather random and established by convention rather than logic; for example, what kind of movement would the accusative in "Ich bin stolz auf dich" (I'm proud of you) convey? Also remember that while "zu" can be used to indicate direction with nouns that have an article ("Ich fahre zur Schweiz" as opposed to "Ich fahre nach Berlin") it always takes the dative, regardless of implied dynamism or stasis. I'm pretty certain that's how the rules work, however as a disclaimer I'd like to point out I'm not a native German (or English, for that matter) speaker. I hope I could be of help :)
I find this one really confusing, all definitions I can find of "kamen" say is is "came".
Additionally, the English translation "We arrived from the airport" makes no sense to me. One must arrive "at" a destination, no?
Why is this not "We came from the airport"?
I don't entirely agree "arriving from somewhere" is wrong. I may not be the most common phrasing when one does not specify where he is arriving, but still please consider "We arrived home just now from the airport" or, from Oxforddictionaries.com in the examples for "arrive": "Youngsters [...] who have just arrived in the city from overseas" (emphasis added). In any case, yes, "we came from the airport" is also a valid translation and is now no more reported as wrong.
Without context, it's impossible to know if the speaker intends "We came from the airport" or "We were coming from the airport." So, again, why is the latter marked wrong?
I am not sure if "we are coming from the airport" should be marked as inncorrect
It should be marked wrong because the form of the verb given in the example is first person plural, simple past tense NOT preset tense. German would render "We are coming from..." as "Wir KOMMEN vom..."
Ok, now "came from" is correct ! Maybe I had a spelling error when I answered this earlier in this exercise and got it wrong and the correction stated that the answer was "arrived from..."