"They have allowed this already."
Translation:Han permitido esto ya.
I've seen "ya" at the beginning of a sentence far more often than anywhere else. So, "¿Ya han permitido esto?" should be accepted. Ellos is optional.
Your translation is just fine but it's not included in the database.
Because ya han permitido = have already allowed and han permitido ... ya = have allowed ... already
I'm not sure about this, but since "ya" can mean either already or now, word order might make a difference as to which one would be understood.
"Ellos ya lo han permitido esto." Sounds a bit strange, but is it correct? Can it be used?
I'm not a native speaker, but I don't think you'd have both lo and esto in the same sentence. That would be "they have already allowed it this." In English we'd have either it or this, but not both.
They have already allowed it = Ya lo han permitido.
They have already allowed this = Ya han permitido esto.
Hopefully Duolingo is giving the most common word order. I'm not sure that this is true for this sentence.