I like to thaw rodents by just leaving them sit out at room temperature for a few hours. I used to thaw in hot water, but after a few rats burst when being constricted, I changed my ways real quick...lol.
It is perfectly fine to feed your snake in his/her cage. I wait to feed until it is dark that way the snake knows that anything that comes into the tank after dark is food and anything that comes into the tank during daylight hours (i.e. my hands) is not food. I think they are less apt to refuse food if offered it when it is dark since that is their natural hunting hours.