To kill a mouse- just take it by the base of the tail and swing into a hard surface. It should kill it INSTANTLY. You'll know by it urinating.

To Thaw- either leave it out all day, OR for faster thawing, I use hot water. I make sure that my mice are all the way thawed by giving them a nice little mouse massage. If I feel any cold spots, then they are not thaw. I dry the mice off afterwards with a towel and touch up with the blow dryer.