It wasn't that the earring was in the wrong ear, it was MISSING because the Thing couldn't duplicate non-organic material. Her suspicions were double confirmed when she asked about the earring and he reached for the wrong ear.
He wasn't taken over by the alien until after they entered the alien ship.
As written, Kate was supposed to unambiguously die, walking off into the freezing wasteland. The studio changed it to leave her fate up in the air, presumably for a possible sequel.