"We passed the mosque."
Translation:Wir kamen an der Moschee vorbei.
Because that's how you say it in German.
vorbei is not a preposition, but you need some kind of preposition here before the noun; vorbei is used together with an in this situation.
Ich gehe an der Schule vorbei (I walk past the school), wir kommen am Postamt vorbei (we'll pass the post office), etc.
Why is the definite article in Dative Case? Shouldn't it be using Accusative Case because of the moving verb "gehen"?
Wir gingen an die Moschee would be "We went to the mosque": to a point touching it.
But here you just passed it: Wir gingen an der Moschee vorbei; "we went past the mosque" -- you passed a point that was located "at the mosque", but that point was not the destination of motion.
dative versus accusative is not about "no motion" versus "motion"; the accusative is used when the point is the destination of motion in some way.
Compare: er lief im Stadion "he ran in the stadium" (round and round in the stadium) and er lief ins Stadion "he ran into the stadium" (from outside the stadium to its inside) -- both involve motion, but only one of them has "in the stadium" as the destination of the motion.
What's the difference between vorbeikommen and vorbeigehen? The Duden seems to say they are synonymous, but is there a different implication to using one or the other? In English, for example, "we're coming by" would imply that you are coming close to the mosque on your way to somewhere else, but you plan to stop in and say hi, or whatever. But "we're going by" would imply that you will be passing near it, but won't stop. Is the same the case for German?