"What are you looking for?"
Translation:Vad letar du efter?
I guess you already realized that leker means 'plays'. The system tries to match what you input to the closest accepted answer, which means you may be shown things that are not taught in the course. Since your answer included är and efter, it was matched to the accepted answer Vad är ni ute efter?, which is like 'What are you after?' in English – it's a very idiomatic way of saying it in Swedish, but, it's only an accepted answer and not taught in the course.
Yes, it's literally 'What are you out for?'
Vad är det ni letar efter? is not an accepted translation. I agree it's a very good and idiomatic Swedish sentence, but we're a bit more literal in this course, since we're trying to teach grammar, so we'd say it corresponds better to 'What is it that you're looking for?'
I think it's only with abstract, general things that we leave efter out. If you say Jag letar hus or Jag letar jobb, you're looking for 'any' house/job (or at least it's pretty general). But if you're looking for a specific house/job, (huset/jobbet) I think it sounds wrong without the preposition.
You know that questions invert the subject/verb order. The subject really wants to stay with the verb, so in the case of a particle verb, it comes between the verb and its particle.
Another example from an earlier lesson: Varför har din dotter på sig rosa strumpor?
We see the same thing in questions with infinitives, e.g. Brukar du skriva brev? The subject comes between the first (auxiliary) verb and the second (infinitive) verb.