i empower Kharox, my opponent tries to counter with not so Not So Fast, can they

No — Not So Fast has no legal target when you Empower Kharox, so your opponent can't counter it.

Empower doesn't choose anything: the source permanent isn't a target of its own Empower ability (Rule 827.1.b.1), and Not So Fast requires an enemy spell or ability that chooses a friendly unit or gear. So there's nothing for them to point it at.

Same goes for the follow-up: Kharox's "when I become Empowered" trigger chooses an opponent (a player, not a unit or gear) and then a unit card in that opponent's trash — neither is a "friendly unit or gear" on the board, so that trigger can't be countered with Not So Fast either. They need a hard counter for abilities, or they wait and answer the unit you play from their trash.