Lisalippy:
39.  The answer is a phrase which means "just the thing".  It also featured in very early radios - try following up on crystal sets.
86.  This is the nickname of a very famous broadcasting organisation.  You will then see how the clue fits in neatly.
89.  Captain Cooker is the animal.  Then a word for a very long time.  Then a word for appointment (as in job).  The whole thing is a sort of airmail (not exactly what you would think of first!)
Paul