Are "Identify this manga" or "Identify this anime" questions on topic for the site? I'm wondering if we could incorporate a similar policy as that on SciFi.SE.
Agreeing with @JNat, I think the SF policy is a very good one for a site which has a medium. You may catch a glimpse of an anime or manga somewhere and think it's good, and then try to find it again. Or you may want to reread that one manga you read at a bookstore when you were bored, but you don't remember the name, just the general theme / specific traits about the characters (this is the case for me, currently).
No, they should definitely be off topic.
I wrote a rather huge essay on this topic on Gaming.SE. Rather than re-post it here, I will just link to that one. All of the points remain the same whether applied to games, anime, movies, etc.