The Parthenon was a church from 1204 until 1456, when Athens was taken by General Mohammed the Conqueror, the Turkish sultan,
who established a mosque in the building and used the Acropolis as a fortress.(A) who established a mosque in the building and used the Acropolis as.
-> Correct. Who modifies sultan and has verb established and used. "as" is used to describe the function/role acropolis did.
(B) who, establishing a mosque in the building, used the Acropolis
like -> Incorrect. "like" should not be used to describe the function/role acropolis did.
(C) who, when he
had established a mosque in the building, used the Acropolis
like -> Incorrect. had established renders the sequence of the events illogical. It depicts that mosque was established first, then athen was taken by sultan.
(D) who
had established a mosque in the building, using the Acropolis
to be -> Incorrect. same error of option "C". "Using to be" is unidiomatic
(E) establishing a mosque in the building and using the Acropolis as
-> Incorrect. This complete sentence is acting as a verbing modifier for the verb of the previous dependent clause, but does not makes sense with the subject of the clause.