Does the KSC Range Safety Officer (RSO) have the ability to abort (destruct) the Falcon 9 first stage on its return to launch site? If so, at what point(s) in the trajectory does this ability exist?
The Range Safety Officer? Nowadays no, because Falcon 9 uses the Automated Flight Safety System (AFSS) (spaceflightinsider.com link)
However, AFSS can destruct the Falcon during landing. In fact this is crucial for Falcon heavy. From the spaceflightinsider.com article linked above:
Additionally, AFSS can support multiple objects in simultaneous flight, which is crucial for companies like SpaceX, which plans to land multiple first stage cores for its Falcon Heavy vehicle at nearly the same time.
From the Florida Today article Only on Falcon 9: Automated system can terminate SpaceX rocket launches:
SpaceX wants to land the two side boosters back at Cape Canaveral, while the middle booster flies on to a ship at sea, so all that three can be recovered and potentially reused. But current Range systems can’t track more than one returning booster.
“If you want to fly multiple boosters back, they have got to be autonomous,” said Monteith. “Otherwise, they’ve got to put them in the ocean.”
Of course, this implies that before AFSS was introduced, the Range Safety Officer had the ability to destruct the Falcon 9 during landing if necessary.