Timing of Babylon's (B) and Halicarnassus' special abilities?
Babylon has a clarification in the rules that says:


  Clariﬁcation :
  - during the sixth turn, the player can therefore play both cards they have in hand. If the second stage of the Wonder is not built, the
  Babylon player can then build it on their sixth turn and then play the
  seventh card instead of discarding it.


Halicarnassus has the following clarification:


  Clariﬁcation : this special action is taken at the end of the turn in
  which the stage is built. If players discard cards on that turn (for
  example, during the 6th turn of an age), the player can also choose
  from among those cards.


I'd say from that that Babylon's power basically all happens "during the sixth turn", and so Halicarnassus can take advantage of any of Babylon's discards.  There isn't really a ghostly extra seventh turn getting created by Babylon's Wonder.