Firstly, you have a cool concept with great potential but it definitely need a lot of polishing to do.
The dialogues should be separated into different paragraphs for an easier reading experience. Putting 3-4 dialogues from three different characters in the same para is confusing and it makes reading a chore.
And you need to take your time to do some research if you want the story to feel serious and logical, since crime novels are complicated with a lot of different elements involved.
The criminal psychology, behavior and their mindset aside you need to be able to present a strong and compelling cases with enough clues and evidences or lack thereof to keep the readers interested.
Take the first case for example, the criminal confessed very easily to Barbara's taunts which are nothing much. A serial killer who killed many without leaving any evidence or fingerprints behind will be much too smart to fall for Barbara's simple provocations.
That too when a precinct full of detectives couldn't get anything out of him will have a great mental fortitude to blurt out confessions in anger.
And he definitely wont leave the dead body in his own car trunk.
And coming to the other detectives, putting aside their judgments and complaints towards Barbara, which could be argued considering Barbara's family background. But them blaming Barbara for cursing them for getting a case with no evidences to work with with is way too childish and immature. And that's not just one detective either. William crying over a celebrity's death because he is a fan paints a very unreliable picture for a homicide detective. I'm not saying they aren't allowed to cry or grieve but that should be done in a proper way without comprising their character and integrity as a police officer.
Sorry if I'm too harsh, my intention is not to bring you down but only with honest criticism will you grow as an author. And remember, no matter what anybody says, including me, keep writing and rewriting and write and rewrite again. That's how you'll grow. And read a lots, preferably the genre you are interested in so you can see how you could do better.
All the best.