He never asked the cop where the scene of the crime was, so they knew that he had murdered his wife.
The poison was in the ice. The survivor girl didn't give time for the ice to melt. Whilst the dead girl waited until the ice melted which meant that the poison was released into her drink.
1. Jack is not the murderer, because he is the brother of the murderer. 2. Dan can't be the murderer since he ran a marathon, and the murderer recently had his leg amputated, and wouldn't be running a marathon of any magnitude that quickly. 3. Ben is not the murderer if he just met Jack, since Jack and the murderer grew up together. 4. This leaves Jeff and Mike. Since Jeff is still alive (he wants to install a new computer next week, present tense) he must be the murderer. Mike also didn't grow up with Jack. It has been determined that Jack, Dan and Jeff are all alive. Ben must also be alive since Jeff plans to install Ben's computer next week. This means that Jeff killed Mike.