"Do you believe in love at first sight?"
Translation:Glaubst du an Liebe auf den ersten Blick?
1) Word order in yes-no questions
To form a yes-no question, German reverses the word order - the inflected verb comes first in a yes-no question. English, by contrast, often uses the word "do" in questions.
Statement: Du glaubst. ( You believe.)
Question: Glaubst du? (Literally: Believe you?. Proper English: Do you believe?)
2) glauben an + accusative = to believe in
With verbs, German and English sometimes use different prepositions. With "glauben" (to believe), German uses "an" and English uses "in".
Ex. Ich glaube an Gott. (I believe in God).
3.) "Love at first sight" is a fixed expression. The German equivalent is also a fixed expression: "Liebe auf den ersten Blick" (literally: love at the first sight).
Hope that helped :)
Glaubst du an Liebe auf den ersten Blick? (literally: Believe you in love at the first sight?)
Suppose you couldn't say something like: "Glaubst du an die Liebe des ersten Blicks?" Or could you?
No, that sounds weird. The english equivalent would be "Do you believe in the love of the first sight?".
Is a glance considered motion, thus the use of accusative rather than dative?
According to my Oxford DE-EN dictionary and the Duden online dictionary, it seems it is not because of the motion, but to give a reason, so “auf + [accusative]”.
Ref: https://www.duden.de/rechtschreibung/auf_Praeposition#Bedeutung5 (5th use: zur Angabe des Grundes, der Voraussetzung)
Do I really need to include the article before ersten here? I probably wouldn't say the article if I was saying it IRL.
Yes, you have to include it. I can't explain why you don't need it in english, but here, the "erster Blick" needs a defining article, since it is the first sight and not any first sight.