if my opponent uses kharox to play a unit from my trash. and i use temporal breach on it. what happens? who gets it? why?

The outcome likely holds, but the answer says the impossible play instruction is 'ignored' under 359.3.e.6, and 1.5 now calls instructions impossible for circumstantial reasons 'Negated', so the wording must change.

If your unit is in the opponents base: the unit is banished for good — it stays in banishment, and neither you nor your opponent gets it. You remain the unit's owner even though your opponent played it from your trash via Kharox — ownership never changes (Rule 127.1). When Temporal Breach resolves, it banishes the unit and then instructs its owner (you) to play it to the same location — which is your opponent's base. You can't legally play a unit to a location you don't control (Rule 355.2.a), so that instruction is impossible and is negated (Rule 359.3.e.6). The banishment stands. If your unit is on a Battlefield controled by the opponent: the unit becomes yours again, gets played to that battlefield and a combat showdown is staged vs the units your opponent still has there. And if your opponent moved away with the other unit(s) after stealing with Kharox, it would be a non-combat showdown at that Battlefield.

Wrong ruling on the BF controled by opponent.

If your unit is in the opponents base: the unit is banished for good — it stays in banishment, and neither you nor your opponent gets it. You remain the unit's owner even though your opponent played it from your trash via Kharox — ownership never changes (Rule 127.1). When Temporal Breach resolves, it banishes the unit and then instructs its owner (you) to play it to the same location — which is your opponent's base. You can't legally play a unit to a location you don't control (Rule 355.2.a), so that instruction is impossible and is ignored (Rule 359.3.e.6). The banishment stands. If your unit is on a Battlefield controled by the opponent: the unit becomes yours again, gets played to that battlefield and a combat showdown is staged vs the units your opponent still has there. And if your opponent moved away with the other unit(s) after stealing with Kharox, it would be a non-combat showdown at that Battlefield.