Is there an official distance between airliners that is acceptable under these circumstances, e.g. 1,000 feet?
Approach-Landing or Takeoffs one behind the other:
Anything up to big--behind big... normally 3 miles...
Anything up to big--behind "jumbo" or "heavy" big... normally 5 miles...
Runway clearances -- same runway:
Landing traffic completely clear
Take-off traffic: airborne/clear of the surface (and GA - unable to abort/re-land on the same surface)
INTERSECTIONS: Conflicted traffic physically clear BEYOND the intersection