i believe that karen fielding tries to blackmail adrian carsini and is not murdered. of course, she didn't have much time to do it in, before columbo already had adrian in custody.
Yes, I overlooked her. She would count as a blackmailer who is not murdered. But as you say, Adrian didn't have much time between the blackmail attempt and being caught by Columbo. If Adrian hadn't been caught, do you think he may have murdered Karen?
i don't know. killing her would certainly bring even more suspicion on himself, since who else would have a motive to kill her. however, he also knew that he was columbo's chief suspect anyway. he might have concluded that getting rid of karen would be more useful than harmful, because it would stop her from being able to testify against him.
he clearly states at the end that he is glad to be going to jail rather than deal with karen's blackmail, so we can assume he really, really, REALLY didn't want to marry her.
adrian says to columbo that he wouldve turned himself in either way because "freedom is relative" and he definitely would rather be in jail than be married to her...