Walter hired a Private Investigator to spy on Hanlon, the private investigator knew Eve and used her to bug the phones. Dobs told Columbo he put Eve in Hanlon's office and she ran an errand to Wagner's house. Eve worked in Hanlon's office not at Eric's house. It seems like Hanlon would be more in charge of hiring a secretary for his own office. After paying attention to this they don't really explain how Eve got hired to work for Hanlon maybe Walter Cannell was able to get her hired there.

Now as for the affair, whenever we see Shirley she is either hugging Hanlon holding his hand, or never more than a two feet away from him. Also while the police are trying to figure out who killed her husband she throws them out of her house, don't you think she would want the police to catch the person who murdered her husband? They never tell us if they are having an affair or not so this one is up to the viewer to decide, but I see signs of an affair by watching Hanlon and Shirley interact.

When Columbo and Hanlon are talking in the airport, Columbo says something like, "Now I have to find out someone who might have had a motive to kill the kid." At that moment, Shirley shows up and collapses crying into Hanlon's arms. And Columbo is shown reacting. There's the motive.