Two questions about Corn Snakes.?

I recently purchased a 6 month old snow corn sake about a week ago, My apartment tends to get rather warm when I am at work being I turn off the air, I have a heat lamp on the cage and also lots of shade for the snake and a water bowl with fresh water every morning and night, my first question is should I turn off the lamp when I go to work? (I have a fan across the room to move air around the cage so it doesn’t get so hot) My second question is how often should I feed it and how much I know usually once a week at this age but how big of a pinky? Thawed or frozen?