Does ATC have to maintain separation on diverging aircraft? Say you have an eastbound flight at FL210 that wants to climb and a westbound flight on a converging track at FL220 that wants to descend. There's the minimum required 1000 ft vertical separation. Once the planes have passed each other can ATC clear them to climb/descend right away or do they have to wait until they are 5nm apart before they can break the vertical separation? And what about TCAS? Would it consider that a conflict?
Yes, this is allowed, subject to certain conditions. See FAA Order 7110.65 (the ATC "bible"), section 5-5-7, for the full details.


  ...all other approved separation may be
  discontinued and passing or diverging separation applied when ... Aircraft are on opposite/reciprocal courses and you have observed that they have passed each other; or aircraft are on same or crossing courses/assigned radar vectors and one aircraft has crossed the projected course of the other, and the angular difference between their courses/assigned radar vectors is at least 15 degrees.


That's in the terminal environment; it's still possible in the enroute environment but a bit more restrictive due to the greater aircraft speeds and poorer radar accuracy.