Yes..but I'm not an expert or anything but I've watched enough ID Channel to know that even if the killer took a shower there would be blood around the drain of the shower. Also they mad the point of him cutting his hand on the knife which would have left his blood on her body.
Maybe, but since it was the financial advisor and they had a relationship I don't think it's too out there that he could have took a shower.
Also, the police and prosecution didn't care. To them they had there man right there and case was closed as far as they were concerned.