Was Bates court scene evidence even likely during those times?

What always bothered me during the Bates court scenes is how the witnesses are called from Downton Abbey, and each one of them are grilled on conversations no one else could have possibly heard or have knowledge about other than Bates and the person he was talking to. Such as those between Robert and Bates about his first wife.

Where did they get that information other than if stupid Bates and his martyr complex told them ever possible self incriminating conversation he had?

The nonsense about who bought the rat poison made no sense, because unless he was there to buy it and put it in her food, there is no proof he had anything to do with her death.

And why would the police be paying attention to that Anna visited where the guy was murdered? Why would the police or anyone else be reporting on this to even know who she was to make not that she was even there?

All of this comes across as really sloppy writing on this show.